The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 15 minutes and a standard deviation of 3 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is %. (Round to two decimal places as needed.) (b) The guaranteed time limit is minutes. (Round up to the nearest integer as needed.)

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 15 minutes and a standard deviation of 3 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is %. (Round to two decimal places as needed.) (b) The guaranteed time limit is minutes. (Round up to the nearest integer as needed.)

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 15 minutes
and a standard deviation of 3 minutes.
(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for
half-price. What percent of customers receive the service for half-price?
(b) If the automotive center does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit?
(a) The percent of customers that receive the service for half-price is
%.
(Round to two decimal places as needed.)
(b) The guaranteed time limit is
minutes. (Round up to the nearest integer as needed.)

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