Five Star Convenience Stores has commissioned StatsRUs a sta

Five Star Convenience Stores has commissioned Stats-R-Us, a statistical firm, to survey its customers in order to estimate the mean amount spent per customer. From previous records the standard deviation is believed to be ? = $5.00. In their proposal to Five Star, Stats-R-Us states that they plan to base the estimate for the mean amount spent per customer on a sample size of 100 and use a 95% confidence interval. Five Star

Solution

Let X be the amount spent per customer.

?x = ?

?x = 5

Stats-R-Us:

n = 100

Xmean = ?xi/100

P(Xmean - z(1 - ?/2)*5/10 < ?x < Xmean + z(1 - ?/2)*5/10) = 0.95

P(Xmean - 1.96*0.5 < ?x < Xmean + 1.96*0.5) = 0.95

P(Xmean - 0.98 < ?x < Xmean + 0.98) = 0.95

Five Star