please help will rate Starbucks has found that 23 of custome

please help will rate

Starbucks has found that 23% of customers purchase more than one cup of coffee per day from their shops. Suppose you randomly choose 175 of today\'s Starbucks customers.

Find the probability that no less than 30% of them purchased more than one cup of coffee from Starbucks.

Solution

Here, we treat the point estimate

u = point estimate = 0.23

and

sp = standard deviation = sqrt(p (1-p)/n) = sqrt(0.23*(1-0.23)/175) = 0.031811947

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.3      
u = mean =    0.23      
          
s = standard deviation =    0.031811947      
          
Thus,          
          
z = (x - u) / s =    2.200431178      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.200431178   ) =    0.013888159 [ANSWER]