Answered: Over time a retailer has determined…

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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Question

Over time a retailer has determined that 20% of all customers entering the store will make a purchase.

What probability distribution does the number of customers making a purchase follow and why?
If 40 customers entered the store what is the probability that exactly 15 make a purchase?

In order to increase sales volume the retailer has introduced a new store layout. Over the course of one week they monitored 1500 customers to see if they made a purchase. They are now interested to see if the proportion of customers making a purchase has grown to more than 0.25.

Which probability distribution can be used to determine if the sample proportion has increased to more than 0.25 (i.e. ? Is it valid to use that distribution to make the calculation in this case?
What is the probability that the sample proportion is more than 0.25 if the new layout has not been successful (i.e. p remains equal to 0.2)
From the answer to part d. if the sample proportion from the 1500 customers was , what would this imply about the new layout based on the balance of probability.

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