joes cupcake shop has been working on inventory control issu

joe\'s cupcake shop has been working on inventory control issues. specifically, the shop has been looking tohttp://www.chegg.com/study/qa# standardize the size of the cupcakes. a sample of 40 cupcakes showed that 20 were more than 50 grams. what is the 75% confidence interval for the proportion of cupcakes more than 50 grams?

Solution

p=20/40 = 0.5

Given a=1-0.75 =0.25 ,Z(0.25/2) = Z(0.125) = 1.15 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.5- 1.15*sqrt(0.5*0.5/40) =0.4090845

So the upper bound is

p + Z*sqrt(p*(1-p)/n) = 0.5+ 1.15*sqrt(0.5*0.5/40) =0.5909155