### Analysis of Automotive Center Service TimesThe time taken by an automotive center to complete an oil change service on an automobile approximately follows a normal distribution. The mean time for the service is 19 minutes, with a standard deviation of 2 minutes.#### Problems:1. **Service Guarantee Analysis** - **Given:** The automotive center guarantees customers that the service will not take longer than 20 minutes. - **Condition:** If it does take longer, the customer will receive the service for half-price. - **Question:** What percent of customers receive the service for half-price?2. **Customer Discount Limitation** - **Given:** The automotive center aims to limit discounts to no more than 2% of its customers. - **Question:** How long should the guaranteed time limit be to meet this criterion?#### Solutions:**(a) Percent of Customers Receiving Half-Price Service**To determine the percentage of customers who receive the service for half-price, follow these steps:1. Calculate the z-score for 20 minutes using the formula: \[ z = \frac{X - \mu}{\sigma} \] where \( X = 20 \) minutes, \( \mu = 19 \) minutes (mean), and \( \sigma = 2 \) minutes (standard deviation).2. Substituting the values: \[ z = \frac{20 - 19}{2} = 0.5 \]3. Using a standard normal distribution table or a z-score calculator, find the area to the right of \( z = 0.5 \), which represents the percentage of customers receiving the half-price service. - From the table, \( P(Z > 0.5) \approx 1 - 0.6915 = 0.3085 \).Thus, \( 30.85\% \) of customers receive the service for half-price.**(b) Time Limit for Not More Than 2% Discounts**To ensure that no more than 2% of customers get the service for half-price:1. Determine the z-score that corresponds to the top 2% of a normal distribution. This z-score is approximately \( z = 2.05 \).2. Solve for \( X \) (the guaranteed time limit) using the z-score formula: \[ X = z\sigma + \mu

Answered: Image /qna-images/answer/52664556-9fd8-436a-8182-69df349b5472.jpg

Answered: (a) The automotive center guarantees…

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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A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, µ, of car rented in the U.S. this year. The consumer group has reason to believe that the mean monthly mileage of cars rented in the U.S. this year is different from last year’s mean, which was 2700 miles. The group plans to do a statistical test regarding the value of µ. It chooses a random sample of monthly mileages and computes the mean of the sample to be 2565 miles and the standard deviation to be 800 miles. What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test? H0: µ is ____ __? __ H1: µ is ____ __ ? ___ In the context of this test, what is a Type II error? A Type II error is ?________ ___ the hypothesis that µ is ? _____ ? when, in fact, µ is ? ____ Suppose that the group decided to reject the null…
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