Answer:
[tex]n=(\frac{2.58(1.2)}{0.25})^2 =153.36 \approx 154[/tex]
So the answer for this case would be n=154 rounded up to the nearest integer
Step-by-step explanation:
Assuming the following question: It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.25 at the 99% confidence level? The population standard deviation is 1.2. If needed, round your final answer up to the next whole number.
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(1.2)}{0.25})^2 =153.36 \approx 154[/tex]
So the answer for this case would be n=154 rounded up to the nearest integer
Find a6: 1, 1/2, 1/6, 1/24, 1/120, a6, 1/5,040, ...
Answer:
Is the #6 in the row. Is this a riddle
Answer:
its 1/720 i just took it
Step-by-step explanation:
The distance between flaws on a long cable is exponentially distributed with mean 12 m.
a. Find the probability that the distance between two flaws is greater than 15m.
b. Find the probability that the distance between two flaws is between 8 and 20 m.
c. Find the median distance.
d. Find the standard deviation of the distances.
e. Find the 65th percentile of the distances.
The question asks for various measures of an exponentially distributed statistic, the distance between flaws on a cable. To find these, we use formulas specific to the exponential distribution; for example, the median is calculated as ln(2) * mean, and the standard deviation is equal to the mean, computed with the formula σ = √variance = √mean.
Explanation:The problem can be modeled using the exponential distribution in statistics. The exponential distribution is often used to model the time elapsed between events in a Poisson point process, or in our case, the distance between the flaws in the cable.
The probability that the distance between two flaws is greater than 15m can be calculated using the formula:https://brainly.com/question/37170119
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In this problem, we're calculating properties of an exponential distribution representing the distances between flaws in a cable. The probability that a given distance is more than 15m is 22.31%, and between 8m and 20m is 48.57%. The median distance is around 8.317m, the standard deviation is 12m, and the 65th percentile is about 14.791m.
Explanation:In this problem, the distance between flaws on a long cable is exponentially distributed with a mean of 12 m. That means the lambda (λ) parameter's rate of occurring flaws per meter is 1/mean, or approximately 0.0833.
For a given exponential distribution, the probability that a random variable X is greater than x is given by P(X > x) = e^(-λx). So, to find the probability that the distance between flaws is greater than 15 m, we substitute 15 for x to get P(X > 15) = e^(-0.0833 * 15) approximately equals 0.2231 or 22.31%. The probability that the distance between two flaws is between 8 and 20 m will be P(8 < X < 20) = P(X < 20) - P(X < 8) which equates to (1 - e^(-0.0833 * 20)) - (1 - e^(-0.0833 * 8)). This calculates to approximately 0.4857 or 48.57%. From the properties of the exponential distribution, the median distance can be calculated using the formula ln2/λ, so the median is approximately 8.317 m. The standard deviation of an exponential distribution is the reciprocal of λ, which is simply the mean (μ). So the standard deviation is also 12 m. The 65th percentile of an exponential distribution can be calculated using the formula: -ln(1 - p) / λ where p is the percentile in decimal form. So the 65th percentile is -ln(1 - 0.65) / 0.0833 ≈ 14.791 m. Learn more about Exponential Distribution here:https://brainly.com/question/33722848
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You are doing marketing research about yogurt consumption. Based on your previous research, you feel sure that the population standard deviation of the number of yogurts consumed per year is 6. In other words, σ is known and σ = 6. You take a sample of 50 consumers and the sample mean is 32 yogurts consumed per year. In other words, = 32. You want to develop a confidence interval for μ푥(the population mean) such that you are 90% confident that the true value of μ lies within the interval.1. What is the value of ?훼
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
From the information given
1) x = 32
σ = 6
n = 50
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645
Margin of error = 1.645 × 6/√50 = 1.4
Confidence interval = 32 ± 1.4
The lower end of the confidence interval is
32 - 1.4 = 30.6
The upper end of the confidence interval is
32 + 1.4 = 33.4
Integrated circuits consist of electric channels that are etched onto silicon wafers. A certain proportion of circuits are defective because of "undercutting," which occurs when too much material is etched away so that the channels, which consist of the unetched portions of the wafers, are too narrow. A redesigned process, involving lower pressure in the etching chamber, is being investigated. The goal is to reduce the rate of undercutting to less than 5%. Out of the first 1000 circuits manufactured by the new process, only 35 show evidence of undercutting. Can you conclude that the goal has been met? Find the P-value and state a conclusion.
Answer:
There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.
P-value=0.01923.
Step-by-step explanation:
We have to test the hypothesis that the proportion of defective circuits is under 5%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]
We will assume a level of significance of 0.05.
The sample, of size n=1000, has 35 defecteive circuits, so the sample proportion is:
[tex]p=35/1000=0.035[/tex]
The standard error is calculated as if the null hypothesis is true, so it is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1000}}}=\sqrt{0.0000475}=0.007[/tex]
The z-statistic can be calculated as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.035-0.050+0.5/1000}{0.007}=\dfrac{-0.0145}{0.007}= -2.07[/tex]
For this one-tailed test, the P-value is:
[tex]P-value=P(z<-2.07)=0.01923[/tex]
As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected. There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.
The diagonal of a square has length 10√2. Find the area of the square.
Answer: [tex]A = 100[/tex] square unit
Step-by-step explanation:
The formula for calculating the area of a square when the diagonal is given is :
[tex]Area = d^{2} / 2[/tex]
That is :
[tex]A = \frac{(10\sqrt{2})^{2}}{2}[/tex]
[tex]A = \frac{100(2)}{2}[/tex]
[tex]A = 100[/tex] square unit
Find the circumference of the circle with the given radius. Round to the nearest tenth. Use 3.14 for π.
r = 8 cm
Step-by-step explanation:
Circumference of the circle= 2πr
=2×3.14×8 cm
= 50.24cm
= 50.2 cm
Answer:
50.27
rounded : 50.3
Step-by-step explanation:
2 times 3.14 times 8
hope this helped
brainliest is appreciated :)
If ax + y=23, 3x - y = 9, and x =8, what is the value of a ?
Answer:
a = 1
Step-by-step explanation:
x = 8
3x - y = 9
3(8) - y = 9
24 - y = 9
-y = 9 - 24
-y = -15
y = 15
ax + y = 23
a(8) + 15 = 23
8a = 23 - 15
8a = 8
a = 8/8
a = 1
. upper left chamber is enlarged, the risk of heart problems is increased. The paper "Left Atrial Size Increases with Body Mass Index in Children" (International Journal of Cardiology [2009]: 1–7) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.4 mm and a standard deviation of 4.2 mm. (a) Approximately what proportion of healthy children have left atrial diameters less than 24 mm? (b) Approximately what proportion of healthy children have left atrial diameters between 25 and 30 mm? (c) For healthy children, what is the value for which only about 20% have a larger left atrial diameter? [4] Suppose that the mean value of interpupillary distance (the distance between the pupils of the left and 2. right eyes) for adult males is 65 mm and that the population standard deviation is 5 mm. Suppose that a random sample of 100 adult males is to be obtained. (a) what is the probability that the sample mean distance ¯x for these 100 will be between 64 and 67 mm?
Answer:
Part 1
(a) 0.28434
(b) 0.43441
(c) 29.9 mm
Part 2
(a) 0.97722
Step-by-step explanation:
There are two questions here. We'll break them into two.
Part 1.
This is a normal distribution problem healthy children having the size of their left atrial diameters normally distributed with
Mean = μ = 26.4 mm
Standard deviation = σ = 4.2 mm
a) proportion of healthy children have left atrial diameters less than 24 mm
P(x < 24)
We first normalize/standardize 24 mm
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (24 - 26.4)/4.2 = -0.57
The required probability
P(x < 24) = P(z < -0.57)
We'll use data from the normal probability table for these probabilities
P(x < 24) = P(z < -0.57) = 0.28434
b) proportion of healthy children have left atrial diameters between 25 and 30 mm
P(25 < x < 30)
We first normalize/standardize 25 mm and 30 mm
For 25 mm
z = (x - μ)/σ = (25 - 26.4)/4.2 = -0.33
For 30 mm
z = (x - μ)/σ = (30 - 26.4)/4.2 = 0.86
The required probability
P(25 < x < 30) = P(-0.33 < z < 0.86)
We'll use data from the normal probability table for these probabilities
P(25 < x < 30) = P(-0.33 < z < 0.86)
= P(z < 0.86) - P(z < -0.33)
= 0.80511 - 0.37070 = 0.43441
c) For healthy children, what is the value for which only about 20% have a larger left atrial diameter.
Let the value be x' and its z-score be z'
P(x > x') = P(z > z') = 20% = 0.20
P(z > z') = 1 - P(z ≤ z') = 0.20
P(z ≤ z') = 0.80
Using normal distribution tables
z' = 0.842
z' = (x' - μ)/σ
0.842 = (x' - 26.4)/4.2
x' = 29.9364 = 29.9 mm
Part 2
Population mean = μ = 65 mm
Population Standard deviation = σ = 5 mm
The central limit theory explains that the sampling distribution extracted from this distribution will approximate a normal distribution with
Sample mean = Population mean
¯x = μₓ = μ = 65 mm
Standard deviation of the distribution of sample means = σₓ = (σ/√n)
where n = Sample size = 100
σₓ = (5/√100) = 0.5 mm
So, probability that the sample mean distance ¯x for these 100 will be between 64 and 67 mm = P(64 < x < 67)
We first normalize/standardize 64 mm and 67 mm
For 64 mm
z = (x - μ)/σ = (64 - 65)/0.5 = -2.00
For 67 mm
z = (x - μ)/σ = (67 - 65)/0.5 = 4.00
The required probability
P(64 < x < 67) = P(-2.00 < z < 4.00)
We'll use data from the normal probability table for these probabilities
P(64 < x < 67) = P(-2.00 < z < 4.00)
= P(z < 4.00) - P(z < -2.00)
= 0.99997 - 0.02275 = 0.97722
Hope this Helps!!!
You and a friend are selling lemonade. You sell three times as many cups as your friend. What percent of the cups sold were sold by your friend? Explain.
Answer:
Step-by-step explanation:
Friend sells x cups
You sell 3x cups
Total cups sold:: 4x
Ans: x/4x = 1/4 = 25%
Final answer:
The fraction of cups sold by your friend is x/4x, which gives us 25% of the total sales when converted to a percentage.
Explanation:
To find out what percent of the cups sold were sold by your friend, we can set up a simple ratio.
Let's assume your friend sold x cups.
According to the problem, you sold three times as many cups, so you sold 3x cups.
The total number of cups sold is the sum of the cups you both sold, which is x + 3x = 4x cups.
Now, we want to find out what fraction of the total sales x represents.
Since your friend sold x cups out of the total 4x, the fraction is x/4x.
To convert this fraction to a percentage, we multiply it by 100%.
Therefore, the percentage of cups sold by your friend is (x/4x) × 100% = 25%.
This calculation shows that your friend sold 25% of the cups.
An article in the Journal of Materials Engineering (Vol 11, No. 4, 1989, pp. 275-282) reported the results of an experiment to determine failure mechanisms for plasma-sprayed thermal barrier coatings. The failure stress for one particular coating (NiCrAlZr) under two different test conditions is as follows:
Failure stress ( times 10^6 Pa) after nine 1-hr cycles: 19.8, 18.5, 17.6,16.7, 16.7, 14.8, 15.4, 14.1, 13.6
Failure stress ( times 10^6 Pa) after six 1-hr cycles: 14.9, 12.7, 11.9, 11.4, 10.1,7.9
(a) What assumptions are needed to construct confidence intervals for the difference in mean failure stress under the two different test conditions? Use normal probability plots of the data to check these assumptions.
(b) Perform a hypothesis test to determine if the mean failure stress of the two different test conditions is the same at the 0.05 significance level.
(c) Confirm that the P-value of this test is 0.001.
Answer:
Step-by-step explanation:
Hello!
You have two variables of interest
X₁: failure stress of a NiCrAlZr coating after nine 1-hr cycles.
X₂: failure stress of a NiCrAlZr coating after six 1-hr cycles.
a)
To be able to estimate the difference between the means using a confidence interval, you need that both variables have a normal distribution and to determine whether or not the population variances are equal.
If the population variances are equal, σ₁²=σ₂², you can use a pooled variance t-test
If the population variances are different, σ₁²≠σ₂², you have to use Welch's t-test
Using α: 0.05
The normality test for X₁ shows a p-value of 0.7449 ⇒ You can assume it has a normal distribution.
The normality test for X₂ shows a p-value of 0.9980 ⇒ You can assume it has a normal distribution.
The F-test for variance homogeneity shows a p-value of 0.6968 (H₀:σ₁²=σ₂²) ⇒You can assume both population variances are equal.
b) and c)
You need to test if both population means are the same, the hypotheses are:
H₀: μ₁=μ₂
H₁: μ₁≠μ₂
α: 0.05
[tex]t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{8*4.28+5*5.62}{9+6-2} }= \sqrt{4.7953}= 2.189= 2.19[/tex]
[tex]t_{H_0}= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } = \frac{(16.36-11.48)-0}{2.19*\sqrt{\frac{1}{9} +\frac{1}{6} } } = 4.23[/tex]
The distribution of this test is a t with 13 degrees of freedom and the test is two-tailed, so to calculate the p-value you have to do the following:
P(t₁₃≤-4.23)+P(t₁₃≥4.23)= P(t₁₃≤-4.23)+[1-P(t₁₃<4.23)]= 0.000492 + (1-0.999508)= 2*0.000492= 0.000984≅ 0.001
The p-value: 0.001 is less than α: 0.05, the decision is to reject the null hypothesis.
I hope it helps!
How many inches is 50cm?
Answer:
Step-by-step explanation:
Answer:
19.5 inches or 19.685 inches for length
Step-by-step explanation:
50•0.39. 50÷3
19.5. 19.685
how to convert centimeters to inches:
multiply the centimeter by 0.39. example 10•0.39= 3.9 inches.
If you want centimeters to inches as length, then divide the centimeters by 3. example: 10÷3= 3.3333333333 inches
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k. Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 10, 0 and negative 8, 2.
Answer:
Sorry about that answer, some people are plain rude, but the correct answer is -5.
Step-by-step explanation:
Hope this Helps! Good Luck!
Answer: k=-5 is correct because if you were to divide -10/-2 it would give you -5
I hope this simplifies your question for the answer.
State the conclusion based on the results of the test. The standard deviation standard deviation in in the pressure required to open a certain valve is known to be sigma equals 1.1 psi. σ=1.1 psi. Due to changes in the manufacturing process, the quality-control manager feels that the pressure pressure variability variability has changed changed. The null hypothesis was not rejected not rejected. Choose the correct answer below. A. There is is sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has changed changed. B. There is is sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has not changed. C. The standard deviation standard deviation in in the pressure has not changed. D. There is not is not sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has not changed. E. There is not is not sufficient evidence that the standard deviation standard deviation in in the pressure required to open a certain valve has changed changed. F. The standard deviation standard deviation in in the pressure has changed changed.
Answer:
B
Step-by-step explanation:
Null hypothesis is not rejected if the test statistics show that the difference between observed and expected value is not significant and any difference is only due to chance.
So there is sufficient evidence from statistics that null hypothesis is true and the standard deviation in the pressure required to open a certain valve has not changed.
since evidence has to be there when null hypothesis is tested, optionC, D and E are rejected.
There is no change in standard deviation so option A and F are rejected.
If y varies directly as x, find k if y = 27 and x = 3.
Answer:
k=9
Step-by-step explanation:
The formula for direct variation is
y = kx
We know y and x
27 = k*3
Divide each side by 3
27/3 = 3k/3
9 =k
How do I work this problem-×+6×=10
Answer:
add -x to 6x to get 5x then divide by 5 to get 2 x is 2
Step-by-step explanation:hope this helps god bless
Step-by-step explanation:
I think you have to find value of x
-x + 6x = 10
5x = 10
x = 10 / 5 = 2
x = 2
Law firm averages 149 cases per year with a standard deviation of 14 points. Suppose the law firm's cases per year are normally distributed. Let X= the number of cases per year. Then X∼N(149,14). Round your answers to THREE decimal places.
Answer: the z- score when x= 186 is 2.643
the mean is 149
this z score tells you that x= 186 is 2.643 standard dev. to the right of the mean
2/3 divided by blank equals
What is the difference of the means of the distributions? 15 30 45 60
Answer:
The difference is 15.
Step-by-step explanation:
30-15=15
45-30=15
60-45=15
Answer:
I agree the difference is 15.
Step-by-step explanation:
The sum of number times 3 and 15
Answer:
3x+15
Step-by-step explanation:
When it says "the sum of a number three times", it means 3x, because the x stands for multiplication and the problem says the sum sum is between 3x and the number 15. So your equation is 3x+15. Hope this helps ;)
2. Find the Area of the triangle.
as do
12 yd
15 yd
Given:
The base of the triangle = 15 yd
The height of the circle = 12 yd
To find the area of the triangle.
Formula
The area of the triangle is
[tex]A=\frac{1}{2} bh[/tex]
where, b be the base of the triangle
h be the height of the triangle
Now,
Putting, b= 15 and h=12 we get,
[tex]A=\frac{1}{2} (15)(12)[/tex] sq yd
or, [tex]A = 90[/tex] sq yd
Hence,
The area of the triangle is 90 sq yd.
Answer:
A =90 yd^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
A = 1/2(15)*12
A =90 yd^2
Figure ABCD is a parallelogram.
What are the lengths of line segments AB and BC?
3
-2
в
• AB = 4, BC = 16
AB = 4; BC = 8
AB = 10; BC = 20
• AB = 10; BC = 28
y
+
6
Given:
Given that ABCD is a parallelogram.
The length of AB is 3y - 2.
The length of BC is x + 12.
The length of CD is y + 6.
The length of AD is 2x - 4.
We need to determine the length of AB and BC.
Value of y:
We know the property that opposite sides of a parallelogram are congruent, then, we have;
[tex]AB=CD[/tex]
Substituting the values, we get;
[tex]3y-2=y+6[/tex]
[tex]2y-2=6[/tex]
[tex]2y=8[/tex]
[tex]y=4[/tex]
Thus, the value of y is 4.
Value of x:
We know the property that opposite sides of a parallelogram are congruent, then, we have;
[tex]AD=BC[/tex]
Substituting the values, we get;
[tex]2x-4=x+12[/tex]
[tex]x-4=12[/tex]
[tex]x=16[/tex]
Thus, the value of x is 16.
Length of AB:
The length of AB can be determined by substituting the value of y in the expression 3y - 2.
Thus, we have;
[tex]AB=3(4)-2[/tex]
[tex]=12-2[/tex]
[tex]AB=10[/tex]
Thus, the length of AB is 10 units.
Length of BC:
The length of BC can be determined by substituting the value of x in the expression x + 12.
Thus, we have;
[tex]BC=16+12[/tex]
[tex]BC=28[/tex]
Thus, the length of BC is 28 units.
Hence, the length of AB and BC are 10 units and 28 units respectively.
The SAT and ACT college entrance exams are taken by thousands of students each year. The mathematics portions of each of these exams produce scores that are approximately normally distributed. In recent years, SAT mathematics exam scores have averaged 480 with standard deviation 100. The average and standard deviation for ACT mathematics scores are 18 and 6, respectively. (a) An engineering school sets 555 as the minimum SAT math score for new students. What percentage of students will score below 555 in a typical year? (Round your answer to two decimal places.)
Answer:
77.34% of students will score below 555 in a typical year
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
SAT:
[tex]\mu = 480, \sigma = 100[/tex]
(a) An engineering school sets 555 as the minimum SAT math score for new students. What percentage of students will score below 555 in a typical year?
This is the pvalue of Z when X = 555. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{555 - 480}{100}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a pvalue of 0.7734.
77.34% of students will score below 555 in a typical year
An experienced ice skater spins on the ice, creating a perfect circle with a diameter of 8 feet. What is the circles radius?
Answer:
radius-4
Step-by-step explanation:
the radius is half of the diameter
Identify the value for the variable.
What is the value of x in this simplified expression?
7-9 · 7-3 = 7x
x =
What is the value of y in this simplified expression?
StartFraction 11 Superscript negative 4 Baseline Over 11 Superscript negative 8 Baseline EndFraction = 11 Superscript y
y =
Answer:
x= -12 y= 4
Step-by-step explanation:
Answer:
Y=4
x=-12
Step-by-step explanation:
A person measures the contents of 25 pop cans and finds the mean content to be 12.1 fluid ounces with a standard deviation of 0.2 ounces. Construct a 99% confidence interval for the average fluid content of a can.
Answer:
The 99% confidence interval for the average fluid content of a can is between 11.54 and 12.66 fluid ounces.
Step-by-step explanation:
We are in posession of the sample's standard deviation, so we use the student t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995([tex]t_{995}[/tex]). So we have T = 2.797
The margin of error is:
M = T*s = 2.797*0.2 = 0.56
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 12.1 - 0.56 = 11.54 fluid ounces.
The upper end of the interval is the sample mean added to M. So it is 12.1 + 0.56 = 12.66 fluid ounces.
The 99% confidence interval for the average fluid content of a can is between 11.54 and 12.66 fluid ounces.
The owner of Get-A-Away Travel has recently surveyed a random sample of 337 customers to determine whether the mean age of the agency's customers is over 20. The appropriate hypotheses are Upper H 0: muequals20, Upper H Subscript a Baseline : mu greater than 20. If he concludes the mean age is over 20 when it is not, he makes a __________ error. If he concludes the mean age is not over 20 when it is, he makes a __________ error.
Answer:
On this case we want to test if the mean age of the agency's customers is over 20, so the system of hypothesis would be:
Null hypothesis: [tex]\mu \leq 20[/tex]
Alternative hypothesis: [tex]\mu >20[/tex]
If he concludes the mean age is over 20 when it is not, he makes a type I error . If he concludes the mean age is not over 20 when it is, he makes a Type II error error.
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.
Solution to the problem
On this case we want to test if the mean age of the agency's customers is over 20, so the system of hypothesis would be:
Null hypothesis: [tex]\mu \leq 20[/tex]
Alternative hypothesis: [tex]\mu >20[/tex]
If he concludes the mean age is over 20 when it is not, he makes a type I error . If he concludes the mean age is not over 20 when it is, he makes a Type II error error.
When the travel agency owner concludes the mean age is over 20 when it's not, it's called a Type I error. If he concludes it's not over 20 when it is, it is a Type II error.
The scenario described involves a hypothesis test concerning the mean age of customers at a travel agency. When the travel agency owner incorrectly concludes that the mean age is over 20 when in fact it is not, he is making a Type I error. Conversely, if he concludes that the mean age is not over 20 when it actually is, that would be a Type II error. Understanding the consequences of these errors is critical in statistics because they affect decision-making processes based on data analysis.
ktoś mi to rozwiarze pls
a)
[tex]2a+(3a-7)=2a+3a-7=5a-7[/tex]
b)
[tex](2x-3)+x=2x-3+x=3x-3[/tex]
c)
[tex]7-(5x+4)=7-5x-4=3-5x[/tex]
d)
[tex]3x-(y-2x)=3x-y+2x=5x-y[/tex]
e)
[tex]-(3a+6)-4=-3a-6-4=-3a-10[/tex]
f)
[tex]-(x-2y)-3x=-x+2y-3x=2y-4x[/tex]
g)
[tex](2p-1)+(3+5p)=2p-1+3+5p=7p+2[/tex]
h)
[tex](4-2x)-(7x-2)=4-2x-7x+2=6-9x[/tex]
i)
[tex]-(2x-1)+(3x+1)=-2x+1+3x+1=x+2[/tex]
j)
[tex](2m+4n)+(m-0,5n)=2m+4n+m-0,5n=3m+3,5n[/tex]
k)
[tex](4a-7b)-(2a+3b)=4a-7b-2a-3b=2a-10b[/tex]
l)
[tex]-(2p-r)-(2r-p)=-2p+r-2r+p=-p-r[/tex]
Solutes in the bloodstream enter cells through osmosis, which is the diffusion of fluid through a semipermeable membrane. Let C = C(t) be the concentration of a certain solute inside a particular cell. The rate at which the concentration inside the cell is changing is proportional to the difference in the concentration of the solute in the bloodstream and the concentration within the cell. Let k be the constant of proportionality. Suppose the concentration of a solute in the bloodstream is maintained at a constant level of L gm/cubic cm. Find the differential equation that best models this situation. (Use C for the concentration within the cell, not C(t).)
Answer:
since the rate at which concentration inside the cell is proportional to the difference in the concentration of the solute in the blood stream and the concentration within the cell, then the rate of change of concentration within the cell is equals to K(L-C).
Thus, the required differential equation is Δc/Δt = K( L - C ).
Step-by-step explanation:
The differential equation that models solute diffusion in osmosis is dC/dt = k*(L - C), representing the idea that the rate of change of the solute's concentration within the cell is proportional to the difference between the external and internal concentrations.
The differential equation that models this situation based on osmosis is expressed as dC/dt = k*(L - C), where C is the concentration of a solute within the cell, L is the constant level concentration in the bloodstream, and k is the constant of proportionality.
This equation is a simple expression of the rate of change being proportional to the difference between the outside and inside concentration levels. In this case, the rate of change of the concentration of solutes, dC/dt, is proportional to the difference between the concentration outside the cell, L, and the concentration inside the cell, C. The constant of proportionality is k.
This differential equation is a first order linear differential equation and represents processes that occur widely in nature, including in the diffusion of solutes through membranes in osmosis.
Learn more about Differential Equation here:
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Yesterday, a flower stand sold a dozen bouquets of flowers, each of which sold for $10. Today, the stand made the same amount of money but the price of a bouquet was increased to $12. How many bouquets were sold today
Answer:
The answer is ten bouquets
Step-by-step explanation:
1 dozen is 12 if you were multiply 12 by 10 you would get 120. Now multiply 10 by twelve instead you get the same answer
Final answer:
When the price of each bouquet increased from $10 to $12, the flower stand sold 10 bouquets to make the same total sales of $120 as the previous day.
Explanation:
The question at hand involves a basic mathematical calculation of how changes in price affect the number of units sold to achieve the same total revenue. If a flower stand sold a dozen bouquets for $10 each yesterday, they made $120 in total sales (12 bouquets imes $10 per bouquet). Today, with the price increase to $12 per bouquet, we need to find out how many bouquets were sold to still make $120 in total sales. The calculation is as follows:
Total Sales = Number of Bouquets Sold imes Price per Bouquet
We know that the Total Sales should still be $120, and the Price per Bouquet is now $12. Therefore:
$120 = Number of Bouquets Sold imes $12
Number of Bouquets Sold = $120 / $12
Number of Bouquets Sold = 10 bouquets
Thus, the flower stand sold 10 bouquets today to make the same amount of money as yesterday after increasing the price to $12 each.
Suppose the number of inches of rainfall each year in a city is normally distributed. For a random sample of years, the confidence interval (3.9,7.7) is generated. Find the margin of error
Answer:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Or equivalently:
[tex]\bar X \pm ME[/tex]
For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula:
[tex]ME= \frac{Upper -Lower}{2}= \frac{7.7-3.9}{2}= 1.9[/tex]
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Or equivalently:
[tex]\bar X \pm ME[/tex]
For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula:
[tex]ME= \frac{Upper -Lower}{2}= \frac{7.7-3.9}{2}= 1.9[/tex]