SOLUTION: According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. What proportion of the samples

Question 1183155: According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. What proportion of the samples will have less than 15% of customers who will make a purchase after visiting the website?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
this is asking what proportion of samples of 50 will have 7 or fewer customers who made a purchase?
that is asking what is the probability that with a 15% base rate 0.14 or fewer will make a purchase?
this is z=(0.14-0.15)/sqrt(0.15*0.85/50)
< -0.01/0.0505
< -0.1980
That probability is 0.4215
-
Can use a normal approximation as a rough check.
mean is np=7.5
variance is np(1-p)=6.375
sd is sqrt (V)=2.525
and get a similar result.

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