Answer:
Step-by-step explanation:
This is a binomial distribution because the probabilities are either that of success or failure.
If probability of success, p = 3/8 = 0.375, then probability of failure, q = 1 - p = 1 - 0.375 = 0.625
The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = represents the probability of failure.
n represents the number of trials or sample.
n = 8
13) P(x = 3) = 8C3 × 0.375^3 × 0.625^(8 - 3) = 0.28
14) P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03
15) P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11
16) P(x = 5) = 8C5 × 0.375^5 × 0.625^(8 - 5) = 0.1
17) P(x ≥ 1) = 1 - P(x < 1)
P(x < 1) = P(x = 0)
P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023
P(x ≥ 1) = 1 - 0.023 = 0.977
18) P(x ≥2) = 1 - P(x < 2)
P(x < 2) = P(x = 0) + P(x = 1)
P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023
P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11
P(x ≥ 2) = 1 - (0.023 + 0.11) = 0.867
19) P(x ≥ 6) = P(x = 6) + P(x = 7) + P(x = 8)
P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03
P(x = 7) = 8C7 × 0.375^7 × 0.625^(8 - 7) = 0.005
P(x = 8) = 8C8 × 0.375^8 × 0.625^(8 - 8) = 0.0004
P(x ≥ 6) = 0.03 + 0.005 + 0.0004 = 0.0354
20) P(x ≥ 7) = P(x = 7) + P(x = 8)
P(x ≥ 7) = 0.005 + 0.0004 = 0.0054
21) P(x ≤ 6) = 1 - P(x = 8)
P(x ≤ 6) = 1 - 0.0004 = 0.9996
22) P(x ≤ 6) = 1 - [P(x = 7) + P(x = 8)]
P(x ≤ 6) = 1 - (0.005 + 0.0004) = 0.9946
The probabilities are listed below:
The probability of success of exactly 3 successes is 5.27 %.The probability of success of exactly 6 successes is 0.28 %.The probablity of success of exactly 1 success is 37.5 %.The probablity of success of exactly 5 successes is 0.74 %.The probability of success of at least 1 success is at most 37.5 %.The probability of success of at least 2 successes is at most 14.1 %.The probablity of success of at least 6 successes is at most 0.28 %.The probability of success of at least 7 successes is at most 0.10 %. The probability of success of at most 7 successes is at least 0.10 %.The probability of success of at most 6 successes is at least 0.28 %.If each trial represents an independent event, then the probability of success of a given number of consecutive trials ([tex]p_{T}[/tex]) in defined by the following formula:
[tex]p_{T} = p^{n}[/tex] (1)
Where:
[tex]p[/tex] - Success probability for a sole event.[tex]n[/tex] - Number of consecutive events.If we know that [tex]p = \frac{3}{8}[/tex], then the probabilities associated to a given number of trials:
1) 3 successes
[tex]p_{3} = \left(\frac{3}{8} \right)^{3}[/tex]
[tex]p_{3} = \frac{27}{512}[/tex]
The probability of success of exactly 3 successes is 5.27 %.
2) 6 successes
[tex]p_{6} = \left(\frac{3}{8} \right)^{6}[/tex]
[tex]p_{6} = \frac{729}{262144}[/tex]
The probability of success of exactly 6 successes is 0.28 %.
3) 1 success
[tex]p_{1} = \frac{3}{8}[/tex]
The probablity of success of exactly 1 success is 37.5 %.
4) 5 successes
[tex]p_{5} = \left(\frac{3}{8} \right)^{5}[/tex]
[tex]p_{5} = \frac{243}{32768}[/tex]
The probablity of success of exactly 5 successes is 0.74 %.
5) At least 1 success
The probability of success of at least 1 success is at most 37.5 %.
6) At least 2 successes
The probability of success of at least 2 successes is at most 14.1 %.
7) At least 6 successes
The probablity of success of at least 6 successes is at most 0.28 %.
8) At least 7 successes
The probability of success of at least 7 successes is at most 0.10 %.
9) At most 7 successes
The probability of success of at most 7 successes is at least 0.10 %.
10) At most 6 successes
The probability of success of at most 6 successes is at least 0.28 %.
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The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased form a nationally known manufacture is actually 1 gallon. You know from the manufacturer’s specifications that the standard deviation of the amount of pant is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of paint per 1-gallon cans is 0.995 gallon.
a. Is there evidence that the mean amount is different from 1.0 gallon (use α = 0.01)?
b. Compute the p-value and interpret the meaning
c. Construct a 99% confidence interval estimate of the population mean amount of paint.
d. Compare the results of (a) and (c). What conclusions do you reach?
Answer:
a) There is no significant evidence to conclude that there there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon.
b) The p-value obtained = 0.076727 > significance level (0.01), hence, we fail to reject the null hypothesis and conclude that there is no significant evidence to conclude that there there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon.
That is, the mean amount of paint per 1-gallon cans is not significantly different from 1 gallon.
c) The 99% confidence for the population mean amount of paint per 1-gallon cans is
(0.988, 0.999) in gallons.
d) The result of the 99% confidence interval does not agree with the result of the hypothesis testing performed in (a) because the right amount of paint in 1-gallon cans, 1 gallon, does not lie within this confidence interval obtained.
Step-by-step explanation:
a) This would be answered after solving part (b)
b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and is always about the absence of significant difference between two proportions being compared. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the null hypothesis is that there is no significant difference in the mean amount of paint per 1-gallon cans and 1 gallon. That is, the mean amount of paint per 1-gallon cans should be 1 gallon.
And the alternative hypothesis is that there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon. That is, the mean amount of paint per 1-gallon cans is not 1 gallon.
Mathematically,
The null hypothesis is
H₀: μ₀ = 1 gallon
The alternative hypothesis is
Hₐ: μ₀ ≠ 1 gallon
To do this test, we will use the z-distribution because we have information on the population standard deviation.
So, we compute the z-test statistic
z = (x - μ)/σₓ
x = the sample mean = 0.995 gallons
μ₀ = what the amount of paint should be; that is 1 gallon
σₓ = standard error = (σ/√n)
σ = standard deviation = 0.02 gallon
n = sample size = 50
σₓ = (0.02/√50) = 0.0028284271 = 0.00283 gallons.
z = (0.995 - 1) ÷ 0.00283
z = -1.77
checking the tables for the p-value of this z-statistic
p-value (for z = -1.77, at 0.01 significance level, with a two tailed condition) = 0.076727
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.01
p-value = 0.076727
0.076727 > 0.01
Hence,
p-value > significance level
So, we fail to reject the null hypothesis and conclude that there is no significant evidence to conclude that there there is significant difference in the mean amount of paint per 1-gallon cans and 1 gallon.
That is, the mean amount of paint per 1-gallon cans is not significantly different from 1 gallon.
c) To compute the 99% confidence interval for population mean amount of paint per 1-gallon paint cans.
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample Mean) ± (Margin of error)
Sample Mean = 0.995 gallons
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 99% confidence interval is obtained from the z-tables because we have information on the population standard deviation.
Critical value = 2.58 (as obtained from the z-tables)
Standard error = σₓ = 0.00283 (already calculated in b)
99% Confidence Interval = (Sample Mean) ± [(Critical value) × (standard Error)]
CI = 0.995 ± (2.58 × 0.00283)
CI = 0.995 ± 0.0073014
99% CI = (0.9876986, 0.9993014)
99% Confidence interval = (0.988, 0.999) in gallons.
d) The result of the 99% confidence interval does not agree with the result of the hypothesis testing performed in (a) because the right amount of paint in 1-gallon cans, 1 gallon, does not lie within this confidence interval obtained.
Hope this Helps!!!
By calculating a z-value and comparing it to the critical value at alpha = 0.01, evidence can be determined. The p-value, as extreme as the calculated one assuming the null hypothesis is true, can be used to interpret the findings. Additionally, a 99% confidence interval estimate can be constructed to provide a range of values that is 99% confident in containing the true population mean amount of paint.
Explanation:a. To determine whether the mean amount of paint contained in 1-gallon cans is different from 1.0 gallon, we can perform a hypothesis test. The null hypothesis (H0) is that the mean amount is 1.0 gallon, and the alternative hypothesis (Ha) is that the mean amount is different from 1.0 gallon. We can perform a z-test using the formula Z = (sample mean - population mean) / (standard deviation / sqrt(sample size)). In this case, the sample mean is 0.995 gallon, the population mean is 1.0 gallon, the standard deviation is 0.02 gallon, and the sample size is 50. By calculating the z-value, we can compare it to the critical value at alpha = 0.01 to determine whether there is evidence to reject the null hypothesis.
b. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. In this case, we can calculate the p-value using the standard normal distribution table or a calculator. If the p-value is less than the significance level (alpha = 0.01), we reject the null hypothesis. The interpretation of the p-value is that there is strong evidence to suggest that the mean amount of paint is different from 1.0 gallon.
c. To construct a 99% confidence interval estimate of the population mean amount of paint, we can use the formula CI = sample mean ± (z-score * (standard deviation / sqrt(sample size))). In this case, the z-score for a 99% confidence level is approximately 2.61. Plugging in the values, we can calculate the confidence interval, which gives us a range of values that we are 99% confident contains the true population mean amount of paint.
d. By comparing the results of (a) and (c), we can draw conclusions about whether the mean amount of paint is different from 1.0 gallon. If the null hypothesis is rejected in (a) and the 99% confidence interval in (c) does not include 1.0 gallon, then we can conclude that there is evidence to suggest that the mean amount is different from 1.0 gallon.
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Parallelogram ABCD is dilated to form parallelogram EFGH. Side AB is proportional to side EF. What corresponding side is proportional to segment AD? Type the answer in the box below. (2 points)
Jack bought 4 dozen eggs at k10 per dozen. 6 eggs were broken .what percent of his money goes waste?
Step-by-step explanation:
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Create a cylinder with a height of 14 cm and a radius of 10 cm.
Create a cylinder with a height of 14 cm and a radius of 10 cm. What can be concluded about the cylinder’s volume when the radius is halved?
The volume is One-fourth of the original.
The volume is One-third of the original.
The volume is One-half of the original.
The volume is twice the original.
Answer:
a on edge2021
Step-by-step explanation:
The volume is One-fourth of the original.
What is a cylinder?"It is a three dimensional structure having two parallel bases joined by a curved surface, at a fixed distance."
The formula of the volume of a cylinder:V = π × r² × h, where 'r' is the radius of the circular base and 'h' is the height of the cylinder.
In the given question,
the radius of the cylinder is 10 cm, and the height is 14 cm.
⇒ r = 10 cm, h = 14 cm
The volume of the cylinder would be,
[tex]V_1=\pi\times 10^2\times 14\\\\V_1=\frac{22}{7}\times 100 \times 14\\\\V_1=4400~~cu.~cm.[/tex]
If the radius is halved, the radius becomes 5 cm.
The new volume of a cylinder would be,
[tex]V_2=\pi \times 5^2\times 14\\\\V_2=\frac{22}{7}\times 25 \times 14\\\\V_2=1100~~cu.~cm.[/tex]
The ratio between the original and the new volume of the cylinder is:
[tex]\Rightarrow \frac{1100}{4400}=\frac{1}{4}\\\\\Rightarrow V_2=\frac{1}{4}V_2[/tex]
This means, the volume is One-fourth of the original.
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To transfer into a particular technical department, a company requires an employee to pass a screening test. A maximum of 3 attempts are allowed at 6-month intervals between trials. From past records it is found that 40% pass on the first trial; of those that fail the first trial and take the test a second time, 60% pass; and of those that fail on the second trial and take the test a third time, 20% pass. For an employee wishing to transfer:
(A) What is the probability of passing the test on the first or second try?
(B) What is the probability of failing on the first 2 trials and passing on the third?
(C) What is the probability of failing on all 3 attempts?
Answer:
a) 0.760
b) 0.048
c) 0.192
Step-by-step explanation:
The step by step solution is attached as an image.
A) The probability of passing the test on the first or second try is 0.760.
That is he pass in the first trial or second trial.
(B) The probability of failing on the first 2 trials and passing on the third is 0.048.
That is the employee fail the first the trial and pass the third trial.
(C) The probability of failing on all 3 attempts is 0.192.
That is the employee fail all the three trial.
The probability of passing on the first or second try is 76%, the probability of failing the first 2 trials and passing on the third is 4.8%, and the probability of failing all 3 attempts is 19.2%.
Explanation:This problem relates to the field of probability. Let's break it down.
For part A, the probability of passing on the first or second try is the sum of the probability of passing on the first try and the product of the probability of failing on the first try and passing on the second. This is calculated as 0.4 + (0.6*0.6) = 0.76 or 76%.
For part B, the probability of failing the first 2 trials and passing on the third is calculated by multiplying the probability of failing the first trial, failing the second, and passing the third: (0.6*0.4*0.2) = 0.048 or 4.8%.
For part C, the probability of failing all 3 attempts is equal to the product of the probability of failing each attempt: (0.6*0.4*0.8) = 0.192 or 19.2%.
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Enter the equation that describes the line in slope-intercept form.
slope =-4, (5,6) is on the line.
Answer:
y = -4x + 26
Step-by-step explanation:
y = mx + b m: slope -4 b: y intercept
pass (5 , 6)
b = y - mx = 6 - (-4) x5 = 6 + 20 = 26
equation: y = -4x + 26
W is less than or equal to 9 and greater than -7
Answer:
(-7, 9]
Step-by-step explanation:
Assuming you want an answer in interval notation:
W is less than or equal to 9 >> [tex]w \leq 9[/tex]
W is greater than- 7 >> [tex]-7 < w[/tex]
Combine the two >> [tex]-7 < w \leq 9[/tex]
So in interval notation, (-7, 9]
equation of the line through (-10,3) and (-8 -8)
Answer:
(-8-3)/(-8+10)= -11/2
y - 3 = -11/2(x+10)
y-3=-11/2x-55
y=-11/2x-52
Step-by-step explanation:
Josephine’s father is 5 times as old as Josephine. In 6 years, he will be only three times as old. How old is Josephine now?
Answer:
Josephine is 6 years old.
Step-by-step explanation:
6 * 5 = 30
12 * 3= 36
Josephine is currently 6 years old.
We are given two conditions about the ages of Josephine and her father.
Josephine’s father is 5 times as old as Josephine currently.
In 6 years, he will be only three times as old as she will be at that time.
Let's let 'J' represent Josephine's current age.
Then her father's current age would be 5J. In 6 years, Josephine will be J+6 and her father will be 5J+6.
According to the second condition, at that time her father's age will be three times Josephine's age.
So, we set up the equation 5J+6 = 3(J+6).
To find Josephine's current age, we solve the equation:
5J + 6 = 3J + 18
Subtract 3J from both sides:
2J + 6 = 18
Now subtract 6 from both sides:
2J = 12
And divide both sides by 2:
J = 6
Therefore, Josephine is currently 6 years old.
emily is 60 inches tall. fernando is 3/4 of emily's height and jasmine is 8/9 of fernando's height. how tall are fernanado and jasmine?
Answer:
fernando is 45 inches tall, and jasmine is 40 inches tall
Step-by-step explanatin
60 divided by 3/4 is 45, 45 divided by 8/9 is 40
Fernando is 45 inches tall, and Jasmine is 40 inches tall.
Emily is 60 inches tall. Fernando is 3/4 of Emily's height:
(60 inches x 3/4 = 45 inches).
Jasmine is 8/9 of Fernando's height:
(45 inches x 8/9 = 40 inches).
MODELING REAL LIFE The total height of the Statue of Liberty and its pedestal is $153$ feet more than the height of the statue. What is the height of the statue?
A picture shows the Statue of Liberty on a pedestal. The total height of the Statue of Liberty and its pedestal is labeled “305 feet”.
Answer: 152
Step-by-step explanation:
305 - 153 = 152
The height of the Statue of Liberty itself, without the pedestal, is 152 feet. This is found by subtracting the pedestal height (153 feet) from the total height (305 feet).
Explanation:The student is asked to determine the height of the Statue of Liberty excluding its pedestal. Given that the total height of the Statue of Liberty including its pedestal is labeled as 305 feet, and the total height is 153 feet more than the height of the statue alone, we can set up the following equation to solve for the height of the statue (let's call it S):
S + 153 = 305
To find the height of the Statue of Liberty without the pedestal, we subtract 153 from both sides of the equation:
S = 305 - 153
S = 152
Therefore, the height of the Statue of Liberty itself is 152 feet.
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A Rhombus with diagonal 1 equal to 5 ft and diagonal 2 equal to 8 ft
Answer:
Area = 20 ft²
Step-by-step explanation:
Area of a thrombus
½ × d1 × d2
½ × 5 × 8
20
Answer:
20 ft squared
Step-by-step explanation:
The area of a rhombus can be calculated by multiplying its diagonals by each other and then halving that product: A = [tex]\frac{1}{2} d_1d_2[/tex]
Here, we know that [tex]d_1[/tex] = 5 and [tex]d_2[/tex] = 8. So, we have the equation: A = [tex]\frac{1}{2} *5*8=(1/2)*40=20[/tex]
Thus, the area is 20 ft squared.
Hope this helps!
Sunhee had four plastic shapes a square, a circle, and a pentagon in how many ways can she line up the four shapes of the circle cannot be next to the square
There are 12 valid arrangements for Sunhee to line up the four plastic shapes so that the circle is not next to the square.
In how many ways can Sunhee line up four plastic shapes (a square, a circle, and a pentagon) if the circle cannot be next to the square?
To solve this problem, we can count the total number of ways to arrange the shapes and then subtract the cases where the circle is next to the square.
1. Total ways to arrange the shapes:
There are 4 shapes, so there are 4! = 24 ways to arrange them.2. Cases where the circle is next to the square:Consider the circle and square together as one unit. We now have 3 units (circle and square, pentagon, and an empty spot).The circle and square can be arranged within this unit in 2! = 2 ways.The total number of ways the four shapes can be arranged with the circle next to the square is 2! × 3! = 12 ways.3. Subtract the cases where the circle is next to the square from the total:24 total ways - 12 ways = 12 ways to line up the shapes with the circle not next to the square.A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability
distribution below?
Answer:
the mean is 3
answer choice D
Step-by-step explanation:
60/20
Hence, the correct answer is 1/5
What is a random variable?A random variable is a numerical valued variable on a defined sample space of an experiment with expressions such as X
How to solve?probability distribution of random variable X is given by,
X 1 2 3 4 5
P(X) 1/5 1/5 1/5 1/5 1/5
mean of probability distribution = [tex]\frac{\sum{P(X)}}{5}[/tex]
= 1/5
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If ST≅SV and m∠SUT=68°, what is m∠TUV?
Answer:
136
Step-by-step explanation:
Take 68 x 2 since the side lengths are equal.
Given the properties of isosceles triangle, where congruent sides have equal opposite angles, and that the given angle ∠SUT = 68°, it implies that ∠TUV also equals 68°.
Explanation:The question involves the principles of geometry, specifically the properties of angles and congruent lines. Given that ST≅SV and m∠SUT = 68°, it means that these two line segments are equal in length and that the angle of SUT is 68 degrees.
Since ST and SV are congruent in an isosceles triangle, the angles opposite these sides are equal. Hence, the measure of ∠SUT and ∠TUV are equal. We know m∠SUT = 68°, so therefore, m∠TUV = 68°.
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Recall the survey you took during the first week of class. One of the questions was “do you agree that it is inappropriate to speak on a cellphone while at a restaurant?” Of the 1913 females that responded to the survey, 1729 agreed with this statement. Of the 1276 males that responded to this survey, 1111 agreed with this statement. Test to see if there is any difference between males and females with respect to how they feel about this issue. Use a significance level of .05.
State the appropriate null and alternative hypotheses.
Calculate the test statistic and report the p-value.
State your conclusion in context of the problem.
Based only on the results of the hypothesis test, would you expect a 95% confidence interval to include 0? Explain.
Calculate and interpret a 95% confidence interval for the difference between males and females.
Answer:
[tex]a) \ H_o:\hat p_f=\hat p_m\\\ \ \ H_a:\hat p_f\neq \hat p_m\\\\b) z\ test=2.925, \ p\ value(two-tail)=0.003444\\\\\\[/tex]
c) Reject H_o since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue.
d. No. Interval does not include zero
e. [tex]CI=[0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]
We are 95% confident that the proportional difference lies between the [0.010444,0.05576] interval.
Step-by-step explanation:
a. The null hypothesis is that there is no difference between males and females with respect to how they feel about this issue:
[tex]H_o:p_m=p_f[/tex]
-The alternative hypothesis is that there is some difference between males and females with respect to how they feel about this issue:
[tex]H_a:p_m\neq p_f[/tex]
where [tex]p_m, \ p_f[/tex] is the proportion of males and females respectively.
b. The proportion of males and females in the study can be calculated as follows:
[tex]\hat p=\frac{x}{n}\\\\\hat p_f=\frac{1729}{1913}=0.9038\\\\\hat p_m=\frac{1111}{1276}=0.8707[/tex]
[tex]\hat p=\frac{x_f+x_m}{n_m+n_f}=\frac{1111+1729}{1276+1913}=0.8906[/tex]
#We then calculate the test statistic using the formula:
[tex]z=\frac{(\hat p_f-\hat p_m)}{\sqrt{\hat p(1-\hat p)(\frac{1}{n_f}+\frac{1}{n_m})}}\\\\\\=\frac{(0.9038-0.8707)}{\sqrt{(0.8906\times0.1094)(\frac{1}{1913}+\frac{1}{1276})}}\\\\\\=2.9250\\\\\therefore p-value=0.001722\\[/tex]
[tex]\# The \ two \ tail \ p-value \ is\\\\=0.01722\times 2\\\\=0.003444[/tex]
c. Since p<0.05:
[tex]p<0.05\\\\0.00344<0.05\\\\\therefore Reject \ H_o[/tex]
Hence, we Reject the Null Hypothesis since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue
d. The 95% confidence interval can be calculated as below:
[tex]CI=(p_f-p_m)\pm z_{\alpha/2}\sqrt{\frac{\hat p_m(1-\hat p_m)}{n_m}+\frac{\hat p_f(1-\hat p_f)}{n_f}}\\\\=(0.9038-0.8707)\pm 1.96\sqrt{0.00008823+0.000045449}\\\\=0.03310\pm 0.02266\\\\=[0.01044,0.05576][/tex]
Hence, the confidence interval does not include 0
e. The 95% confidence interval calculated from above is :
[tex]0.01044<(p_f-p_m)<0.05576[/tex]
Hence, we are 95% confident that the proportional difference will fall between the interval [tex]0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]
The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour. (a-1) At α = .05 in a left-tailed test, would a sample of 16 randomly chosen hours with a mean of 510 and a standard deviation of 50 indicate that the manufacturer’s claim is overstated? Choose the appropriate hypothesis. a. H1: μ < 530. Reject H1 if tcalc > –1.753 b. H0: μ < 530. Reject H0 if tcalc > –1.753 c. H1: μ ≥ 530. Reject H1 if tcalc < –1.753 d. H0: μ ≥ 530. Reject H0 if tcalc < –1.753 a b c d (a-2) State the conclusion. a. tcalc = –1.6. There is not enough evidence to reject the manufacturer’s claim. b. tcalc = –1.6. There is significant evidence to reject the manufacturer’s claim. a b
Answer:
(a) H1: μ < 530. Reject H1 if tcalc > –1.753
(b) t calc = –1.6. There is not enough evidence to reject the manufacturer’s claim.
Step-by-step explanation:
We are given that the manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour.
A sample of 16 randomly chosen hours with a mean of 510 and a standard deviation of 50 is given.
Let [tex]\mu[/tex] = average bags an airport baggage scanning machine can handle
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 530 bags {means that an airport baggage scanning machine can handle an average of more than or equal to 530 bags per hour}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 530 bags {means that an airport baggage scanning machine can handle an average of less than 530 bags per hour}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 510
s = sample standard deviation = 50
n = sample of hours = 16
So, test statistics = [tex]\frac{510-530}{\frac{50}{\sqrt{16} } }[/tex] ~ [tex]t_1_5[/tex]
= -1.60
The value of t test statistics is -1.60.
Now, at 0.05 significance level the t table gives critical value of -1.753 at 15 degree of freedom for left-tailed test. Since our test statistics is more than the critical values of t as -1.60 > -1.753, so we have insufficient evidence to reject our null hypothesis as it will not in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that an airport baggage scanning machine can handle an average of more than or equal to 530 bags per hour.
I don’t understand my homework... and don’t go at me I’m an slow learner I never done this... before... but NOTE I already got the first one...
Answer:
52 weeks
365 days
10 years
100 years
Step-by-step explanation:
Which diagram represents a cylinder with a base area equal to 50Pi square meters?
1. A cylinder with height of 50 meters and volume = 250 pi meters cubed.
2. A cylinder with height 25 meters and volume = 250 pi meters cubed.
3. A cylinder with height 5 meters and volume = 250 pi meters cubed.
Answer: C
Step-by-step explanation:
Answer:The answer Is The Third One On The Right.
Step-by-step explanation:
A common design for a mountain cabin is an A-frame
cabin. A-frame cabins are fairly easy to construct and
the steeply pitched roof line is perfect for helping snow
fall to the ground during heavy winters. Determine the
angle ( between the two sides of the roof of an A-frame
cabin if the sides are both 26 feet long and the base of
the cabin is 24 feet wide.
Answer:
54.98 degrees.
Step-by-step explanation:
In the diagram, the sides of the A-Frame are lengths AB and BC. The width of the cabin is length BC. We are to determine the measure of the angle at B, i.e. the angle between the two sides of the roof.
Using Cosine Rule:
[tex]b^2=a^2+c^2-2acCos B\\Cos B=\dfrac{b^2-a^2-c^2}{-2ac} \\B=arcCos(\dfrac{b^2-a^2-c^2}{-2ac} )\\a=26, b=24, c=26\\B=arcCos(\dfrac{24^2-26^2-26^2}{-2*26*26} )\\=arcCos 0.5739\\B=54.98^0[/tex]
The angle in between the two sides of the roof is 54.98 degrees.
To find the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry and the Pythagorean theorem. The angle is approximately 22.33°.
Explanation:To determine the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry. Since the sides of the roof are both 26 feet long and the base of the cabin is 24 feet wide, we can consider the A-frame cabin as a right triangle. The roof line forms the hypotenuse of the triangle, and the sides of the triangle represent the rafters of the A-frame roof.
Using the Pythagorean theorem, we can find the height of the triangle (which is the distance from the base of the cabin to the point where the roof meets): h^2 = 26^2 - 12^2 = 676 - 144 = 532.
Taking the square root of both sides gives us h ≈ 23.07 feet.
Now, we can determine the angle by using trigonometric functions.
The sine function relates the opposite side (the height) to the hypotenuse (the roof line). So, sin(θ) = h / 26, where θ is the angle we want to find. Solving for θ gives us θ ≈ 22.33°.
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512 = (m + 7) ^ 3/2
It’s algebra!!!
Answer:
m = 57
Step-by-step explanation:
If we assume your equation is supposed to be ...
512 = (m +7)^(3/2)
we can raise both sides to the 2/3 power to get ...
512^(2/3) = m +7
64 = m +7
57 = m . . . . . . subtract 7
Salim has 5 boxes of paint jars. Each box has the same number of paint jars. His teacher gives him 6 more paint jars. Now he has 41 paint jars. How many paint jars were in each box
Answer:
7 jars per box
Step-by-step explanation:
He now has 41 jars. How many did he have before his teacher gave him 6?
Well, 41-6=35. He had 35 jars before his teacher gave him more.
It says there was an equal amount of jars in each box. There are 5 boxes. Divide the total amount of jars (35) by the amount of boxes to find out how many jars are in each box.
35 jars / 5 boxes = 7 jars / box
In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 26 recent loans is taken. The average calculated from this sample is 7.20%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.7%. Compute 95% and 99% confidence intervals for the population mean 30-year fixed mortgage rate.
Answer:
The 95% CI is (6.93% , 7.47%)
The 99% CI is (6.85% , 7.55%)
Step-by-step explanation:
We have to estimate two confidence intervals (95% and 99%) for the population mean 30-year fixed mortgage rate.
We know that the population standard deviation is 0.7%.
The sample mean is 7.2%. The sample size is n=26.
The z-score for a 95% CI is z=1.96 and for a 99% CI is z=2.58.
The margin of error for a 95% CI is
[tex]E=z\cdot \sigma/\sqrt{n}=1.96*0.7/\sqrt{26}=1.372/5.099=0.27[/tex]
Then, the upper and lower bounds are:
[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.27=6.93\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.27=7.47[/tex]
Then, the 95% CI is
[tex]6.93\leq x\leq 7.47[/tex]
The margin of error for a 99% CI is
[tex]E=z\cdot \sigma/\sqrt{n}=2.58*0.7/\sqrt{26}=1.806/5.099=0.35[/tex]
Then, the upper and lower bounds are:
[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.35=6.85\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.35=7.55[/tex]
Then, the 99% CI is
[tex]6.85\leq x\leq 7.55[/tex]
Multiply: (-3/10)(-2/9)
Answer:
1/15
Step-by-step explanation:
Which graph represents the solution set of the inequality Negative 14.5 less-than x?
A. A number line going from negative 15 to negative 11. An open circle is at negative 13.5. Everything to the right of the circle is shaded.
B. A number line going from negative 15 to negative 11. A closed circle is at negative 14. Everything to the right of the circle is shaded.
C. A number line going from negative 15 to negative 11. An open circle is at negative 14.5. Everything to the right of the circle is shaded.
D. A number line going from negative 15 to negative 11. A closed circle is at negative 15. Everything to the right of the circle is shaded.
The solution of the inequality -14.5 < x represents graph which is correct option C
What is inequality?
Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
-14.5 < x
x > -14.5
A number line going from negative 15 to negative 11. An open circle is at negative 14.5. Everything to the right of the circle is shaded.
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the specification for a plastic handle calls for a length of 6.0 inches +- .2 inches. The standard deviation of the process is estimated to be 0.05 Inches. what are the upper and lower specification limits for this product.
Answer:
a)
USL = 6.2 inches
LSL = 5.8 inches
b) Cp = 1.33
Cpk = 0.67
c)
Yes it meets all specifications
Step-by-step explanation:
The specification for a plastic handle calls for a length of 6.0 inches ± .2 inches. The standard deviation of the process is estimated to be 0.05 inches. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.1 inches. What is the Cp and Cpk for this process? Is this process capable of producing the desired part?
Given that:
Mean (μ) = 6.1 inches, Standard deviation (σ) = 0.05 inches and the length of the plastic handle is 6.0 inches ± .2
a) Since the length of the plastic handle is 6.0 inches ± .2 = (6 - 0.2, 6 + 0.2)
The Upper specification limits (USL) = 6 inches + 0.2 inches = 6.2 inches
The lower specification limits (LSL) = 6 inches - 0.2 inches = 5.8 inches
b) The Cp is given by the formula:
[tex]Cp=\frac{(USL-LSL)}{6\sigma} =\frac{(6.2-5.8)}{6*0.05} =1.33[/tex]
The Cpk is given by the formula:
c)
The upper specification limit lies about 3 standard deviations from the centerline, and the lower specification limit is further away, so practically all units will meet specifications
[tex]Cpk=min(\frac{USL-\mu}{3\sigma},\frac{\mu -LSL}{3\sigma})=min(\frac{6.2-6.1}{3*0.05},\frac{6.1-5.8}{3*0.05})=min(0.67,2)=0.67[/tex]
Final answer:
The upper specification limit for the plastic handle is 6.2 inches, and the lower specification limit is 5.8 inches, with these limits defining the acceptable range for the handle length.
Explanation:
The specification for a plastic handle is given as a length of 6.0 inches with a tolerance of ± 0.2 inches. This means the upper specification limit (USL) and the lower specification limit (LSL) are defined by adding and subtracting the tolerance to the target length respectively. The process standard deviation is 0.05 inches, but this does not affect the USL and LSL directly; it's a measure of the process variation.
The USL and LSL are calculated as follows:
USL = Target Length + Tolerance = 6.0 inches + 0.2 inches = 6.2 inchesLSL = Target Length - Tolerance = 6.0 inches - 0.2 inches = 5.8 inchesThese limits are the range within which the plastic handle lengths should fall according to the given specifications.
covert 4.5 yards to inches what is the answer ?
Answer:
162 inches
Step-by-step explanation:
To get the answer you would have to know how many inches are a yard. The answer is 36. So you would have to multiply 4.5 by 36.
Answer:
Conversions :
1 ft = 12 in.
3 ft = 1 yard
Step-by-step explanation:
[tex]4.5 yards (\frac{3 ft}{1 yard} ) ( \frac{12 in.}{1 ft} ) = 162[/tex]
Find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8.
Answer:
[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]
Step-by-step explanation:
Integrate your function with respect to x to get the non-differentiated form.
[tex]\int(5x^2+9x-7)dx=\frac{5}{3}x^3+\frac{9}{2}x^2-7x+c\\[/tex]
Plug in your known value of x to get your value for your constant
[tex]f(0) = 8\\ \frac{5}{3}(0^3)+\frac{9}{2}(0^2)-7(0)+c = 8 \\c=8[/tex]
This gives you your function to be
[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]
To find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8, integrate the given function and solve for the constant of integration using the given condition. The resulting equation is f(x) = (5/3)x³ + (9/2)x² - 7x + 8.
Explanation:To find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8, we need to integrate f'(x) to find the equation for f(x). Let's find the antiderivative of 5x² + 9x - 7, which is (5/3)x³ + (9/2)x² - 7x + C. To determine the value of C, we can use the given condition f(0) = 8. Substituting x = 0 into the equation, we get 8 = (5/3)(0)³ + (9/2)(0)² - 7(0) + C. Solving for C, we find that C = 8. Therefore, the equation for f(x) is f(x) = (5/3)x³ + (9/2)x² - 7x + 8.
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Patty is making a poster for science class. She spends. 50 minutes on each. Of 2 days. She completes 1/3 of the poster the first day and another 1/3 the next day what fraction of the poster has she completed so far?
Answer:
She has completed 2/3 of the poster
Explanation:
1/3 of the poster the first day
+
1/3 of the poster the next day
1/3 + 1/3 = 2/3
A manufacturer sells video games with the following cost and revenue functions (in dollars), where x is the number of games sold. Determine the interval(s) on which the profit function is increasing. Upper C (x )equals 0.17 x squared minus 0.00016 x cubed Upper R (x )equals 0.362 x squared minus 0.0002 x cubed
Answer:
Therefore profit function is increasing on the interval (0,3200)
Step-by-step explanation:
The cost function of the manufacturer C(x) is given as:
[TeX]C(x)= 0.17x^{2}-0.00016x^{3}[/TeX]
The Revenue function is also given as:
[TeX]R(x)= 0.362x^{2}-0.0002x^{3}[/TeX]
Profit=Revenue-Cost
Therefore:
P(x)=R(x)-C(x)
[TeX]= 0.362x^{2}-0.0002x^{3}-[0.17x^{2}-0.00016x^{3}][/TeX]
[TeX]= 0.362x^{2}-0.0002x^{3}-0.17x^{2}+0.00016x^{3}[/TeX]
The Profit Function, [TeX]P(x)= 0.192x^{2}-0.00004x^{3}[/TeX]
To determine the point where the function is increasing, we take the derivative and examine it's critical points.
The derivative of the profit function is:
[TeX]P^{'}(x)= 0.384x-0.00012x^{2}[/TeX]
Set the derivative equal to zero.
[TeX]0.384x-0.00012x^{2}=0[/TeX]
[TeX]x(0.384x-0.00012x)=0[/TeX]
x=0 or [TeX]0.384-0.00012x=0[/TeX]
x=0 or [TeX]0.384=0.00012x[/TeX]
x=0 or x=3200
Now let's choose 2000 and 4000 as test points.
[TeX]P^{'}(2000)= 0.384(2000)-0.00012(2000)^{2}=288[/TeX]
[TeX]P^{'}(4000)= 0.384(4000)-0.00012(4000)^{2}=-384[/TeX]
Therefore profit function is increasing on the interval (0,3200)
Answer:
The is profit function is increasing on (0, 3200).
Step-by-step explanation:
Given
C(x) = 0.17x² - 0.00016x³
R(x) = 0.362x² - 0.0002x³
The profit function is given by
P(x) = R(x) - C(x)
P(x) = (0.362x² - 0.0002x³) - (0.17x² - 0.00016x³)
P(x) = 0.362x² - 0.0002x³ - 0.17x² + 0.00016x³
P(x) = 0.192x² - 0.00004x³
The derivative of the profit function is given by
P'(x) = 0.384x - 0.00012x²
Determine the critical number of P(x) to get interval where the profit function is increasing,
Set P'(x) = 0
0.384x - 0.00012x² = 0
x(0.384 - 0.00012x) = 0
x = 0 or 0.384 - 0.00012x = 0
0.384 - 0.00012x = 0
x = 0.384/0.00012 = 3200
Therefore the is profit function is increasing on (0, 3200)