A statistician calculates that 7 of Americans own a Rolls Ro

A statistician calculates that 7% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 527 Americans would be greater than 9%? (Round your answer to 4 decimal places)

Solution

Here,

mean = p = 0.07

The standard deviation of the proportions is

s = sqrt(p(1-p)/n) = sqrt(0.07*(1-0.07)/527) = 0.011114379

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.09      
u = mean =    0.07      
          
s = standard deviation =    0.011114379      
          
Thus,          
          
z = (x - u) / s =    1.799470758      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.799470758   ) =    0.035972123 [ANSWER]