The check-out wait times for Grocery Store A are approximately normal with mean 8 minutes and standard deviation 2 minutes. The check-out wait times for Grocery Store B has an unknown distribution with mean 5 minutes and standard deviation 1 minute. A customer shops at Grocery Store A 16 random times throughout the year and at Grocery Store B 36 random times throughout the year. (a) Find the probability that the customer's mean wait time at Store A for the entire year is less than 9 minutes? (b) Determine the probability that the variance in the customer's wait times at Grocery Store A for the entire year is greater than 7.33, i.e. P(Sž>7.33). (c) Determine the probability that the customer's mean wait time at Grocery Store A for the entire year is less than 2 minutes longer than the mean wait time at Grocery Store B for the entire year, i.e., P(XA – Xg < 2).

The check-out wait times for Grocery Store A are approximately normal with mean 8 minutes and standard deviation 2 minutes. The check-out wait times for Grocery Store B has an unknown distribution with mean 5 minutes and standard deviation 1 minute. A customer shops at Grocery Store A 16 random times throughout the year and at Grocery Store B 36 random times throughout the year. (a) Find the probability that the customer's mean wait time at Store A for the entire year is less than 9 minutes? (b) Determine the probability that the variance in the customer's wait times at Grocery Store A for the entire year is greater than 7.33, i.e. P(Sž>7.33). (c) Determine the probability that the customer's mean wait time at Grocery Store A for the entire year is less than 2 minutes longer than the mean wait time at Grocery Store B for the entire year, i.e., P(XA – Xg < 2).

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 check-out wait times for Grocery Store A are approximately normal with mean 8 minutes and
standard deviation 2 minutes. The check-out wait times for Grocery Store B has an unknown
distribution with mean 5 minutes and standard deviation 1 minute. A customer shops at Grocery
Store A 16 random times throughout the year and at Grocery Store B 36 random times throughout
the year.
(a) Find the probability that the customer's mean wait time at Store A for the entire year is less
than 9 minutes?
(b) Determine the probability that the variance in the customer's wait times at Grocery Store
A for the entire year is greater than 7.33, i.e. P(S3>7.33).
(c) Determine the probability that the customer's mean wait time at Grocery Store A for the entire
year is less than 2 minutes longer than the mean wait time at Grocery Store B for the entire year,
i.e., P(XA – XB < 2).

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