Answer:
She should guarantee a weight of 4.18 pounds.
Step-by-step explanation:
Problems of normally distributed samples can be 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.
In this problem, we have that:
[tex]\mu = 8.6, \sigma = 1.9[/tex]
What weight should she guarantee so that she will have to give her customer's money back only 1% of the time?
She should guarantee the 1st percentile of weights, which is X when Z has a pvalue of 0.01. So it is X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.327 = \frac{X - 8.6}{1.9}[/tex]
[tex]X - 8.6 = -2.327*1.9[/tex]
[tex]X = 4.18[/tex]
She should guarantee a weight of 4.18 pounds.
The turkey farmer should guarantee that her 6-week poults will weigh at least 4.2 pounds to ensure that she will have to give money back only 1% of the time.
Given:
- Mean weight [tex](\( \mu \))[/tex] of poults: 8. 6 pounds
- Standard deviation [tex](\( \sigma \))[/tex] of poults: 1.9 pounds
1. Use the z-score corresponding to the 1st percentile of the normal distribution, which is approximately [tex]\( z_{0.01} \approx -2.3263 \)[/tex].
2. Calculate the guaranteed weight X:
[tex]\[ X = \mu + z_{0.01} \cdot \sigma \] \[ X = 8.6 + (-2.3263) \cdot 1.9 \] \[ X \approx 4.2 \text{ pounds} \][/tex]
Therefore, the turkey farmer should guarantee that her 6-week poults will weigh at least 4.2 pounds to ensure that she will have to give her customers' money back only 1% of the time. This ensures that 99% of the poults will weigh at least 4.2 pounds.
How many games did Lisa score less than 13 points?
(Group of answer choices)
A) 15
B) 7
C) 5
D) 12
Answer:
it's B) 7
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
So if Lisa scored less than 13 points then the answer has to lie in the intervals 1-12. You had 2 from intervals 1-6 and 5 from intervals 7-12 and you get 7
Solve for x:
3x+4=9x+3
3x+4=9x+3
A light bulb factory produces 1,188 light bulbs every hour. Approximately 3.83% of the light bulbs are defective, and do not work. Using the binomial distribution, what is the standard deviation of the number of defective bulbs produced in an hour
Answer:
The standard deviation of the number of defective bulbs produced in an hour is 6.615
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, we have that:
[tex]p = 0.0383, n = 1188[/tex]
What is the standard deviation of the number of defective bulbs produced in an hour
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1188*0.0383*(1-0.0383)} = 6.615[/tex]
The standard deviation of the number of defective bulbs produced in an hour is 6.615
Write the equation of a parabola whose graph
separates the blue points from the red points.
The equation of a parabola that separates the blue points from the red points can be written in the form y = ax² + bx + c, where a, b, and c are constants. The specific coefficients will determine the direction, width, and position of the parabola.
Explanation:To create an equation for a parabola that separates the blue and red points, we need more information about the specific characteristics desired for the parabola. The general form of the equation y = ax² + bx + c allows us to customize the parabola's shape. The coefficient a determines the direction of the parabola (opening upwards or downwards), while b and c influence its horizontal shift and vertical position.
For example, if we want a parabola that opens upwards with its vertex at the origin (0,0) and separates the points above from those below, the equation could be y = ax², where a is a positive constant. If a horizontal shift or translation is needed, adjustments to b and c can be made accordingly.
In summary, the equation of the parabola depends on the specific requirements for separating the blue and red points, and the general form y = ax² + bx + c provides the flexibility to tailor the parabola's characteristics to meet those needs.
Of the 219 white GSS2008 respondents in their 20s, 63 of them claim the ability to speak a language other than English. With 99% confidence, what is the upper limit of the population proportion based on these statistics
Answer:
The upper limit for population proportion is 0.3666
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 219
Number of people who have ability to speak a language other than English, x = 63
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{63}{219} = 0.2877[/tex]
99% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 2.58[/tex]
Putting the values, we get:
[tex] 0.2877\pm 2.58(\sqrt{\dfrac{ 0.2877(1- 0.2877)}{219}})\\\\ = 0.2877\pm 0.0789\\\\=(0.2088,0.3666)[/tex]
is the required 99% confidence interval for population proportion.
Thus, the upper limit for population proportion is 0.3666
Answer:
The upper limit of the 99% confidence interval for the population proportion based on these statistics is 0.3665.
Step-by-step explanation:
We are given that of the 219 white GSS 2008 respondents in their 20's, 63 of them claim the ability to speak a language other than English.
So, the sample proportion is : [tex]\hat p[/tex] = X/n = 63/219
Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion = [tex]\frac{63}{219}[/tex]
n = sample of respondents = 219
p = population proportion
Here for constructing 99% confidence interval we have used One-sample z proportion statistics.
So, 99% confidence interval for the population proportion, p is ;
P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at
0.5% level of significance are -2.5758 & 2.5758}
P(-2.5758 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.5758) = 0.99
P( [tex]-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
P( [tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
99% confidence interval for p = [ [tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]\frac{63}{219} -2.5758 \times {\sqrt{\frac{\frac{63}{219}(1-\frac{63}{219})}{219} } }[/tex] , [tex]\frac{63}{219} +2.5758 \times {\sqrt{\frac{\frac{63}{219}(1-\frac{63}{219})}{219} } }[/tex] ]
= [0.2089 , 0.3665]
Therefore, 99% confidence interval for the population proportion based on these statistics is [0.2089 , 0.3665].
Hence, the upper limit of the population proportion based on these statistics is 0.3665.
Ben ran for president of his class is there a 410 students and he receive 72% of the vote how many students voted for Ben
Answer:
295
Step-by-step explanation:
multiply 410 x .72=295.2
you can not have .2 of a person, so you must round. Normally the question states what to round to, whether up or down, but generally .2 rounds down so: 295
Final answer:
295 students voted for Ben.
Explanation:
To calculate how many students voted for Ben in the class president election, we need to use the percentage of votes he received. Ben received 72% of the total votes from a class of 410 students.
First, convert the percentage to a decimal by dividing by 100:
72% = 72 ÷ 100 = 0.72
Then, multiply this decimal by the total number of students to find out how many voted for Ben:
Number of votes for Ben = 0.72 × 410
Now, we calculate the multiplication:
Number of votes for Ben = 295.2
Since we can't have a fraction of a vote, we'll round down to the nearest whole number. Thus, 295 students voted for Ben.
Which events are independent? A.) you choose 2 different ice cream flavors B.) you study English 20 minutes nightly then you get an A on the next test C.) you draw card from a deck and replace it and draw second D.) you draw card and don’t replace it then you draw another
Answer:
i believe that the answer is A.) but im not 100% sure, im about 65% sure
Step-by-step explanation:
Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter which he finds, to the nearest millimeter, to be 5 centimeters.
To find the area of the circle, Juan uses the formula where A is the area of the circle and r is its radius. He uses 3.14 for π. What value does Juan get for the area of the circle? Make sure you include your units.
Answer:
Step-by-step explanation:
Hi there,
To get started, recall the area of a bound circle formula:
[tex]A = \pi r^{2}[/tex] where r is radius of the circle. However, Juan used an approximate value of π, 3.14. So for our purposes, the formula becomes:
[tex]A=[/tex] [tex](3.14)r^{2}[/tex]
Juan measured the circle's diameter, so we can find radius from diameter first. Radius is simply twice the length of the diameter; from one circle endpoint to the center, to the endpoint across, making a straight line:
[tex]d=2r[/tex] ⇒ [tex]r=\frac{d}{2} = \frac{5 \ cm}{2} = 2.5 \ cm[/tex]
Now plug in to obtain area:
[tex]A = (3.14)(2.5 cm)^{2} =19.625 \ cm^{2}[/tex]
The area is 19.265 centimetres squared.
Cross-sections are the area shapes when you cut through a 3D volume; if you cut through a pipe perpendicular to where it flows, you can see it is a circle! If you cut straight through a cube, it would be a square, etc.
If you liked this solution, hit Thanks or give a Rating!
thanks,
A high school statistics class wants to estimate the average number of chocolate chips in a generic brand of chocolate chip cookies. They collect a random sample of cookies, count the chips in each cookie, and calculate a 95% confidence interval for the average number of chips per cookie (18.6 to 21.3).
The next four statements present four different interpretations of these results. Indicate if each interpretation is valid or invalid.
Interpretation #1: We are 95% certain that each cookie of this brand has approximately 18.6 to 21.3 chocolate chips. --ValidInvalid
Interpretation #2: We expect 95% of the cookies to have between 18.6 and 21.3 chocolate chips. --ValidInvalid
Interpretation #3: We would expect about 95% of all possible sample means from this population to be between 18.6 and 21.3 chocolate chips.--ValidInvalid
Interpretation #4: We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie.ValidInvalid
Write 0.8 as a fraction in the simplest form.
Answer:
4/5
Step-by-step explanation:
.8 is a fourth of 1.0
.20
.40
.60
.80
1.0
since there are five total numbers from that sequence, and .8 is the fourth, the simplest form it could go to is 4/5
The decimal number 0.8 as a fraction in the simplest form is 4/5.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
In this exercise and scenario, we would convert the given decimal number into a fraction as follows;
0.8 = 8/10
By dividing both the numerator and denominator by 2, we have the following
8/10 = 4/5
Read more on fraction here: brainly.com/question/29367657
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how long will it take to earn one dollar at the rate of $10 per hour
Answer:
6 minutes
Step-by-step explanation:
Since it's you have 10 dollars in one hour, and you want to find 1/10th of the dollar value, you'd multiply 1/10th, or 0.1 by the time as well. I converted it into minutes because we're finding a smaller unit of time than 1 hour.
60 min x 1/10 (or 60 min/10)= 6 minutes
I hope this helped!
6 minutes
If it takes 1 hour to earn $10, we convert that 1 hour to 60 minutes. Now we will divide 60 by 10, and that gives you 6. Therefore every 6 minutes you earn $1.
Hope this helps!
The number of ants per acre in the forest is normally distributed with mean 45,289 and standard deviation 12,340. Let X= number of ants in a randomly selected acre of the forest. Round all answers to two decimal places.
Final answer:
Normal distribution characterizes variables like the number of ants per acre, and the Central Limit Theorem helps understand the distribution of sample means. Allele frequencies are calculated by multiplying the number of homozygote ants by two and then dividing by the total number of alleles.
Explanation:
When discussing the number of ants per acre in a forest, you're dealing with a normal distribution, which is a probability distribution that is symmetric about the mean. With a known mean (μ) of 45,289 and a standard deviation (σ) of 12,340, if we let X represent the number of ants in a randomly selected acre, we can make various probabilistic predictions.
The Central Limit Theorem (CLT) applies when considering the sampling distribution of the sample mean. For example, if we have a population with a mean (μ) of 50 and standard deviation (σ) of 4, and take 100 samples each of size 40, the CLT tells us that the sampling distribution of the sample mean will be approximately normally distributed, centered around the population mean (μ), and with a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n). This is because, as per the law of large numbers, the sample means tend to get closer to the population mean as the sample size increases.
When calculating allele frequencies, it's essential to multiply the number of homozygote ants by 2 (as each ant has two alleles) to obtain the number of that allele in the population. The allele frequency is then the number of a specific allele divided by the total number of alleles.
A recent study reported that 1.5 percent of flights are canceled by major air carriers. Consider a simulation with 50 trials designed to estimate the number of canceled flights from a random sample of size 100, where the probability of success, a canceled flight, is 0.015.
Step-by-step explanation:
"Of the following dotplots, which best represents the possible results from the simulation described?"
The sample size is 100, and the probability of success is 0.015, so the expected value is 1.5. Meaning we would expect a dotplot with most of the dots at 1 and 2.
By considering a simulation with 50 trials designed to estimate the number of canceled flights from a random sample of size 100, where the probability of success, a canceled flight, is 0.015. A dot-plot with most of the dots at 1 and 2.
Given:
Sample size (n) = 100
Probability = 0.015
To estimate the number of canceled flights
Expected value = 0.015 x 100
Expected value = 1.5
Therefore, a dot-plot with most of the dots at 1 and 2.
For more information, refer to the link given below:
https://brainly.com/question/14850769
9. When 200 randomly selected car owners are surveyed, it is found that the mean length of time they plan to keep their car is 7.01 years, and the standard deviation is 3.47 years. Calculate the appropriate test statistic to test the claim that the mean for all car owners is less than 7.5 years.
Answer:
The appropriate test statistic to test the claim that the mean for all car owners is less than 7.5 years is -1.997.
Step-by-step explanation:
We are given that 200 randomly selected car owners are surveyed, it is found that the mean length of time they plan to keep their car is 7.01 years, and the standard deviation is 3.47 years.
Let [tex]\mu[/tex] = mean for all car owners.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 7.5 years {means that the mean for all car owners is more than or equal to 7.5 years}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 7.5 years {means that the mean for all car owners is less than 7.5 years}
The test statistics that will be used here is One-sample t test statistics as we don't know about 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 length of time = 7.01 years
s = sample standard deviation = 3.47 years
n = sample of cars = 200
So, test statistics = [tex]\frac{7.01-7.5}{\frac{3.47}{\sqrt{200} } }[/tex] ~ [tex]t_1_9_9[/tex]
= -1.997
Hence, the appropriate test statistic to test the claim is -1.997.
Factor the polynomial completely using the
X method
2 + 16x + 48
Which equivalent four-term polynomial can be created
using the X method?
O2 + 8x + 8x + 48
ox2 - 12x - 4x + 48
x2 + 12x + 4x + 48
ac
0x28x 8x +
() Intro
Answer:
its answer C
Step-by-step explanation:
x² - 12x + 4x + 48
three students are chosen at random find the probability that all three were born on Wednesday
Final answer:
The probability that all three students were born on Wednesday is 1/343.
Explanation:
To find the probability that all three students were born on Wednesday, we need to consider the total number of possible outcomes and the number of favorable outcomes.
There are 7 days in a week, so each student has a 1/7 chance of being born on Wednesday. Since the students are chosen at random and the choices are independent, we can multiply the probabilities together to find the probability that all three students were born on Wednesday:
P(all three born on Wednesday) = (1/7) * (1/7) * (1/7) = 1/343.
F (x) = -3x+5x^2+8 has blank roots.
Answer:
F (x) = -3x+5x^2+8 has complex roots.
Step-by-step explanation:
number of roots?
ok.
f(x) = 5xx - 3x + 8 = 5xx + 5x - 8x + 8 ( I was guessing what numbers would sum to -3)
nope.
ok try discriminant: (-3)^2 - 4*5 * 8 = 9 - 160 < 0
2 complex roots
If the 18th term of a geometric sequence is 177,147 and the 24th term is 129,140,163 what is the 10th term?
Answer:
the term is 2/3(6)n-1
Step-by-step explanation:
Common ratio, r= 6
3rd term=24
Finding first term=
24=a 6^{2}
24=36a
a=24/36
a=2/3
The height of a radio tower is 400 feet, and the ground on one side of the tower slopes upward at an angle of 10degrees. (a) How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 190 feet from the base of the tower? (b) How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 190 feet from the base on the flat side?
Answer:
(a) 412 ft
(b) 276 ft
Step-by-step explanation:
Consider the attached diagram.
(a) The internal angle of triangle RBT at B is 90° -10° = 80°. Since we know lengths RB and BT, we can find the length RT using the law of cosines:
RT² = RB² +BT² -2·RB·BT·cos(80°) = 190² +400² -2·190·400·cos(80°)
RT² ≈ 169,705.477
RT ≈ √169,705.477 ≈ 411.95
The guy wire to the hillside should be about 412 feet long.
__
(b) The Pythagorean theorem can be used to find the shorter wire length.
LM² = LB² +MB²
LM = √(190² +200²) = √76,100
LM ≈ 275.86
The guy wire to the flat side should be about 276 feet long.
2•2•2•n•n using exponents. The product is?
Answer:
2^3 n^2 or 8n^2
Step-by-step explanation:
Which term could have the greatest common factor of 5m squared n squared
Answer: I think it’s B and D on eduinuity 2021
Step-by-step explanation:
The required 5m²2n² is the greatest common factor of (b) 5m⁴n₃ and (d) 15m²n².
What is the greatest common factor?The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of all the given numbers.
For example, the GCF of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.
here,
The terms that could have the greatest common factor of 5m²n² are:
5m⁴n₃, since 5m²n² is a factor of both 5m⁴n³ and 5m²n².
15m²n², since 5m²n² is a factor of both 15m²n² and 5m²2n².
Therefore, the correct options are (b) 5m⁴n₃ and (d) 15m²n².
Learn more about the greatest common factors here: https://brainly.com/question/11221202
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The complete question is given in the attachment below,
The measure of a base angle of an isosceles triangle is 20. What is the measure of the vertex?
Answer:
140 degrees
Step-by-step explanation:
Since this triangle is isosceles, the base angles must be equal. This means that two out of the three angles in the triangle are 20 degrees. Since all of the angles together in a triangle must add up to 180 degrees, the angle of the vertex is 180-20-20=140 degrees. Hope this helps!
Answer:
140
Step-by-step explanation:
The base angle is 20. That means the other base angle is also 20
20+20 = 40
The sum of the angles of a triangle is 180
180-40= 140
That means the third angle must be 140
Researchers are studying rates of homeowners in a certain town. They believe that the proportion of people ages 36-50 who own homes is signifificantly greater than the proportin of people age 21-35 who own homes and want to test this claim. The results of the surverys are: Homeowners Renters Total
Ages 21-35 18 38 56
Ages36-50 40 22 62
TOTAL 58 60 118
What are the null hypothesis and alternative hypothesis for this situation
Answer:
Being p1 the proportion for people of ages 36-50 and p2 the proportion for people of ages 21-35, the null and alternative hypothesis will be:
[tex]H_0: p_1-p_2=0\\\\H_a: p_1-p_2>0[/tex]
Step-by-step explanation:
A hypothesis test on the difference of proportions needs to be performed for this case.
We have two sample proportions and we want to test if the true population proportions differ from each other, usign the information given by the sample statistics.
The claim is that the proportion of people of ages 36-50 who own homes is significantly greater than the proportin of people age 21-35 who own homes.
The term "higher" will define the alternative hypothesis, that is the hypothesis that represents what is claimed. The null hypothesis always include the equal sign, and will state that both proportions do not differ.
Being p1 the proportion for people of ages 36-50 and p2 the proportion for people of ages 21-35, the null and alternative hypothesis will be:
[tex]H_0: p_1-p_2=0\\\\H_a: p_1-p_2>0[/tex]
The null hypothesis (H0) is that the proportion of homeowners ages 36-50 is equal to the proportion of homeowners ages 21-35 (H0: P1 = P2), and the alternative hypothesis (Ha) is that the proportion of homeowners ages 36-50 is greater than that of ages 21-35 (Ha: P1 > P2).
Explanation:To answer the question, the null hypothesis (H0) and the alternative hypothesis (Ha) must be formulated based on the given data about homeownership across different age groups. In this research, the null hypothesis would state that the proportion of homeowners who are ages 36-50 is equal to the proportion of homeowners who are age 21-35. Mathematically, this can be represented as H0: P1 = P2.
The alternative hypothesis is what the researchers are trying to support, which is that the proportion of homeowners who are ages 36-50 is significantly greater than the proportion of homeowners who are age 21-35, represented as Ha: P1 > P2.
It is important to note that a hypothesis test will be used to determine if there is enough statistical evidence to reject the null hypothesis in favor of the alternative hypothesis.
The weight of potato chip bags filled by a machine at a packaging plant is normally distributed with a mean of 15.0 ounces and a standard deviation of 0.1 ounces. What percentage of bags weigh more than 14.8 ounces
Answer:
97.73% of bags weigh more than 14.8 ounces.
Step-by-step explanation:
We are given that the weight of potato chip bags filled by a machine at a packaging plant is normally distributed with a mean of 15.0 ounces and a standard deviation of 0.1 ounces.
Let X = weight of potato chip bags filled by a machine
So, X ~ N([tex]\mu=15.0,\sigma^{2} =0.1^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean weight = 15.0 ounces
[tex]\sigma[/tex] = standard deviation = 0.1 ounces
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, percentage of bags that weigh more than 14.8 ounces is given by = P(X > 14.8 ounces)
P(X > 14.8 ounces) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{14.8-15.0}{0.1}[/tex] ) = P(Z > -2) = P(Z < 2)
= 0.9773 or 97.73%
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.9773.
Hence, 97.73% of bags weigh more than 14.8 ounces.
To find the percentage of bags weighing more than 14.8 ounces, we calculate the z-score for 14.8 ounces and use the normal distribution properties. A z-score of -2 corresponds to 2.28% of bags weighing less, so about 97.72% weigh more.
Explanation:To determine what percentage of potato chip bags weigh more than 14.8 ounces when the mean weight is 15.0 ounces with a standard deviation of 0.1 ounces, we use the properties of the normal distribution. First, we calculate the z-score for 14.8 ounces:
Z = (X - μ) / σ = (14.8 - 15.0) / 0.1 = -2
The z-score tells us how many standard deviations away 14.8 ounces is from the mean. A z-score of -2 indicates that 14.8 ounces is 2 standard deviations below the mean. Using the z-score table or a calculator with normal distribution functions, we find the area to the left of z = -2. This area represents the percentage of bags weighing less than 14.8 ounces. Since we're interested in bags weighing more than 14.8 ounces, we subtract this value from 1 (or 100% if we're working with percentages).
For z = -2, the area to the left is approximately 0.0228 (or 2.28%). Therefore, the percentage of bags that weigh more than 14.8 ounces is about 100% - 2.28% = 97.72%.
Plot the function y(x)=e–0.5x sin(2x) for 100 values of x between 0 and 10. Use a 2- point-wide solid blue line for this function. Then plot the function y(x)=e–0.5x cos(2x) on the same axes. Use a 3-point-wide dashed red line for this function. Be sure to include a legend, title, axis labels, and grid on the plots
In the plot, I have graphed two functions on the same set of axes.
The first function, y(x) = e^(-0.5x) * sin(2x), is represented by a solid blue line with a 2-point line width.
The second function, y(x) = e^(-0.5x) * cos(2x), is shown with a dashed red line with a 3-point line width. Both functions are evaluated for 100 values of x ranging from 0 to 10.
The solid blue line represents the sine function, and the dashed red line represents the cosine function.
The legend, title, axis labels, and grid have been included to make the plot more informative and visually appealing.
In this plot, you can observe the oscillatory behavior of both functions as they decay exponentially with decreasing x.
The legend distinguishes between the two functions, and the grid helps in reading the values accurately.
The choice of line widths and colors enhances the visibility of the two functions, making it easier to compare their behavior over the specified range of x values.
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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 15 bag sample had a mean of 423 grams with a standard deviation of 26. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis.
Answer:
[tex]t=\frac{423-433}{\frac{2.6}{\sqrt{15}}}=-14.896[/tex]
[tex]df=n-1=15-1=14[/tex]
We need to find in the t distribution with df=14 a value who accumulates 0.1 of the area in the left and we got [tex]t_{crit}= -1.345[/tex].
Since our calculated value for the statistic is is so much lower than the critical value we have enough evidence to reject the null hypothesis, and we can conclude that the true mean for this case is significantly less than 433 and then the machine is underfilling.
Step-by-step explanation:
Data given
[tex]\bar X=423[/tex] represent the sample mean
[tex]s=26[/tex] represent the sample standard deviation
[tex]n=15[/tex] sample size
[tex]\mu_o =433[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 433 (underfilling), the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 433[/tex]
Alternative hypothesis:[tex]\mu < 433[/tex]
The statistic is:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Calculate the statistic
[tex]t=\frac{423-433}{\frac{2.6}{\sqrt{15}}}=-14.896[/tex]
Decision rule
The degrees of freedom are:
[tex]df=n-1=15-1=14[/tex]
We need to find in the t distribution with df=14 a value who accumulates 0.1 of the area in the left and we got [tex]t_{crit}= -1.345[/tex]
Since our calculated value for the statistic is is so much lower than the critical value we have enough evidence to reject the null hypothesis, and we can conclude that the true mean for this case is significantly less than 433 and then the machine is underfilling.
A sample of size n = 100 produced the sample mean of ܺത= 16. Assuming the population standard deviation σ= 3, compute a 95% confidence interval for the population mean μ. (b) Assuming the population standard deviation σ= 3, how large should a sample be to estimate the population mean μ with a margin of error not exceeding 0.5 with a 95% confidence interval?
The 95% confidence interval for the population mean based on a sample of 100 with mean 16 and population standard deviation 3 is (15.412, 16.588). For a margin of error not exceeding 0.5, a sample size of 139 is needed.
Explanation:To compute the 95% confidence interval for the population mean μ, we use the formula for a confidence interval which is ȳ ± Z*(σ/√n), where ȳ is the sample mean, σ is the population standard deviation, n is the sample size, and Z is the z-score corresponding to the desired confidence level (for a 95% confidence interval, Z = 1.96).
Plugging the given values into the formula, we get 16 ± 1.96*(3/√100), which simplifies to 16 ± 0.588. Thus, the 95% confidence interval for the population mean μ is (15.412, 16.588).
For the second part of the question, the formula used to find the sample size needed for a certain margin of error (E) at a certain confidence level is n = (Zσ/E)^2. Substituting the given values into this formula, we get n = (1.96*3/0.5)^2 which is equal to 138.384. Since we can't have a fraction of a sample, we round this up to the nearest whole number, so we would need a sample size of 139 to estimate the population mean μ with a margin of error not exceeding 0.5 with a 95% confidence interval.
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To compute a 95% confidence interval for the population mean μ, we can use the formula: Confidence Interval = Sample Mean ± (Z * σ/√n). The 95% confidence interval for the population mean μ is (15.412, 16.588). To estimate the sample size needed to keep the margin of error within 0.5 with a 95% confidence level, we can use the formula: n = (Z^2 * σ^2) / (E^2). We need a sample size of at least 24 to estimate the population mean μ with a margin of error not exceeding 0.5, with a 95% confidence level.
Explanation:To compute a 95% confidence interval for the population mean μ, we can use the formula:
Confidence Interval = Sample Mean ± (Z * σ/√n)
Where Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
For this problem:
Confidence Interval = 16 ± (1.96 * 3/√100)
Simplifying, we get:
Confidence Interval = 16 ± 0.588
Therefore, the 95% confidence interval for the population mean μ is (15.412, 16.588).
To estimate the sample size needed to keep the margin of error within 0.5 with a 95% confidence level, we can use the formula:
n = (Z^2 * σ^2) / (E^2)
Where Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the maximum acceptable margin of error.
For this problem:
n = (1.96^2 * 3^2) / (0.5^2)
Simplifying, we get:
n = 23.532
Therefore, we need a sample size of at least 24 to estimate the population mean μ with a margin of error not exceeding 0.5, with a 95% confidence level.
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Determine which of (a)-(d) form a solution to the given system for any choice of the free parameter. (HINT: All parameters of a solution must cancel completely when substituted into each equation.) 3x1 + 8x2 − 14x3 = 9 x1 + 3x2 − 4x3 = 1
Answer:
Please see attachment
Question:
The options are;
(a) (9 - 2s1, 3 + 3s1, s1)
solution
not a solution
(b) (-4 - 5s1, s1, -(3 + s1)/2)
solution
not a solution
(c) (11 + 10s1, -3 - 2s1, s1)
solution
not a solution
(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)
solution
not a solution
Answer:
The options that form a solution of the given system are;
(b) and (c)
Step-by-step explanation:
Here we have
3·x₁ + 8·x₂ − 14·x₃ = 9
x₁ + 3·x₂ − 4·x₃ = 1
(a) (9 - 2·s₁, 3 + 3·s₁,s₁)
3·(9 - 2·s₁) + 8·(3 + 3·s₁) − 14·s₁ = 4s₁+51
Not a solution
(b) (-4 - 5s₁, s₁, -(3 + s1)/2)
3·(-4 - 5s₁) + 8·(s₁) − 14·-(3 + s1)/2 = 9
(-4 - 5s₁) + 3·(s₁) − 4·-(3 + s1)/2 = 2
Solution
(c) (11 + 10s₁, -3 - 2s₁, s₁ )
3·(11 + 10s₁) + 8·(-3 - 2s₁) − 14·s₁ = 9
(11 + 10s₁) + 3·(-3 - 2s₁) − 4·s₁ = 2
Solution
(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)
3·(6 - 4s1)/3+ 8·s1− 14·-(7 - s1)/4 = 0.5s₁ +30.5
Not a solution
4. Major League Baseball (MLB) has recently been evaluating the timing of various events during games in an effort to improve the pace of a game. MLB wants to know how long a mound visit, defined as when a coach pauses the game to visit the pitcher on the mound, takes on average. MLB randomly selects 100 games over the course of a season, and records the length, in seconds, of every mound visit that occurs in that game. This sample of mound visits can be best described as a
Answer:
cluster sample
Step-by-step explanation:
a)If Paul is risk-loving and his basketball team has a probability of .6 of winning, then Paul would rather bet $10 on his team than $1000. (When Paul bets X, he wins X if his team wins and loses X if his team loses) True or False.
Answer:
FALSE. If he is risk-loving, he will rather bet $1,000 rather than $10.
Step-by-step explanation:
FALSE.
As Paul is risk-loving, he will take more risk, even if there is no more chances of winning if he bets $10 or $1,000. He will focus on the probability of winnings rather than the expected losses.
In this case, the probabilities are the same independently of the amount that Paul bets.