1. Bookstore
A university bookstore claims that 50% of its customers are satisfied with the service and prices.
a. If this claim is true, what is the probability that in a random sample of 600 customers less than 45% are satisfied?
b. If you would reject the bookstore’s claim if the probability computed in a. will be less than 0.05%, how many customers at least should have expressed satisfaction?

a. We denote the (population) probability that is claimed by the bookstore as p(=0.5) and the probability computed by the sample as \hat{p} (=0.45). Then:
b. In this case we have to compute x from P(Z<x)=0.05. From table 3 in appendix B-8 we find x=-1.65. So, we have to solve \hat{p} from the equation: \displaystyle{\frac{\hat{p}-0.50}{\sqrt{0.50(1-0.50)/600}}=-1.65} and we get: \hat{p}=0.466=x/600 and thus the number of customers expressing satisfaction should be at least 280.

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