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e. For the 45 customers, find the probability that their average spent is more than $7.3424. 0.5514 X f. Find the probability that the randomly selected 45 customers will spend more than $330.4080. 0 X g. For part e) and f), is the assumption of normal necessary? Yes No No O h. The owner of Don Mcalds gives a coupon for a free sundae to the 3% of all groups of 45 people who spend the most money. At least how much must a group of 45 spend in total to get the free $1 sundae? 10 2537 X

e. For the 45 customers, find the probability that their average spent is more than $7.3424. 0.5514 X f. Find the probability that the randomly selected 45 customers will spend more than $330.4080. 0 X g. For part e) and f), is the assumption of normal necessary? Yes No No O h. The owner of Don Mcalds gives a coupon for a free sundae to the 3% of all groups of 45 people who spend the most money. At least how much must a group of 45 spend in total to get the free $1 sundae? 10 2537 X

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Statistical Problems and Solutions Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. **a. What is the distribution of \(X\)?** \(X \sim N(\) * Mean (\(\mu\)): **7.4300** * Standard Deviation (\(\sigma\)): **1.5100** **b. What is the distribution of \(\bar{x}\)?** \(\bar{x} \sim N(\) * Mean (\(\mu\)): **7.4300** * Standard Deviation: \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\): **0.0506** *[This answer is incorrect]* **c. What is the distribution of \(\sum x\)?** \(\sum x \sim N(\) * Sum: 334.35 * Sum of squares: \(4617.2\)) *[This answer is incorrect]* **d. What is the probability that one randomly selected customer will spend more than $7.3424?** Probability: **0.7190** *[This answer is incorrect]* **e. For the 45 customers, find the probability that their average spent is more than $7.3424.** Probability: **0.5514** *[This answer is incorrect]* **f. Find the probability that the randomly selected 45 customers will spend more than $330.4080.** Probability: **0** *[This answer is incorrect]* **g. For part e) and f), is the assumption of normal necessary?** **Yes** *[Correct]* **h. The owner of Don Mcalds gives a coupon for a free sundae to the 3% of all groups of 45 people who spend the most money. At least how much must a group of 45 spend in total to get the free sundae?** At least: **$10.2537** *[This answer is incorrect]* ### Explanation of Symbols and Meanings * **\(N(\mu, \sigma)\)**: Normal distribution with mean \(\mu\) and standard deviation \(\sigma\). * **\(\bar{x}\)**: Sample mean. * **\(\sum x\)**: Sum of the sample values. * **\(
Transcribed Image Text:### Statistical Problems and Solutions Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. **a. What is the distribution of \(X\)?** \(X \sim N(\) * Mean (\(\mu\)): **7.4300** * Standard Deviation (\(\sigma\)): **1.5100** **b. What is the distribution of \(\bar{x}\)?** \(\bar{x} \sim N(\) * Mean (\(\mu\)): **7.4300** * Standard Deviation: \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\): **0.0506** *[This answer is incorrect]* **c. What is the distribution of \(\sum x\)?** \(\sum x \sim N(\) * Sum: 334.35 * Sum of squares: \(4617.2\)) *[This answer is incorrect]* **d. What is the probability that one randomly selected customer will spend more than $7.3424?** Probability: **0.7190** *[This answer is incorrect]* **e. For the 45 customers, find the probability that their average spent is more than $7.3424.** Probability: **0.5514** *[This answer is incorrect]* **f. Find the probability that the randomly selected 45 customers will spend more than $330.4080.** Probability: **0** *[This answer is incorrect]* **g. For part e) and f), is the assumption of normal necessary?** **Yes** *[Correct]* **h. The owner of Don Mcalds gives a coupon for a free sundae to the 3% of all groups of 45 people who spend the most money. At least how much must a group of 45 spend in total to get the free sundae?** At least: **$10.2537** *[This answer is incorrect]* ### Explanation of Symbols and Meanings * **\(N(\mu, \sigma)\)**: Normal distribution with mean \(\mu\) and standard deviation \(\sigma\). * **\(\bar{x}\)**: Sample mean. * **\(\sum x\)**: Sum of the sample values. * **\(
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