The local book store has a customer loyalty program that also allows them to tra

Question

The local book store has a customer loyalty program that also allows them to track purchases. According to their records, a sample of 27 customers on the program buy on average 18 books a year, with a population standard deviation of 6 books.

1. The bookstore hired a college student that produced a confidence interval for the mean number of books sold per customer in this sample as (15,21.) What level of confidence was this student using?

2. The Stony Brook University generally wins 60% of the major sporting events they playfootball, softball, soccer- everything. What is the probability, during 60 season games, of winning 40 or more games?

Explanation / Answer

1)margin of error =(21-15)/2=3

here std error of mean =std deviation/(n)1/2 =1.1547

for z=margin of error/std error =3/1.1547=2.598

for above level of confidence =99%

2)here mean =np=60*0.6=36

std deviaiton =(np(1-p))1/2 =3.7947

hence P(X>=40) =1-P(X<=39)=1-P(Z<(39.5-36)/3.7947)=1-P(Z<0.9223)=1-0.8218=0.1782

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