Starbucks has found that 27 of customers purchase more than

Starbucks has found that 27% of customers purchase more than one cup of coffee per day from their shops. Suppose you randomly choose 205 of today\'s Starbucks customers

Question: Find the probability that no less than 32% of them purchased more than one cup of coffee from Starbucks.

Please explain using the z=pbar-p/SQRT(p(1-p)/n)

Solution

Here, the distribution of the sample mean has mean

u = 0.27

s = sqrt(p(1-p)/n) =sqrt(0.27*(1-0.27)/205) = 0.031007474

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.32      
u = mean =    0.27      
          
s = standard deviation =    0.031007474      
          
Thus,          
          
z = (x - u) / s =    1.612514454      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.612514454   ) =    0.053425019 [ANSWER]