Question

A statistician calculates that 7%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 527527 Americans would be greater than 9%9%

Answer 1

0.0359 approximately 0.0360

Explanation:

Mean = 7% = p

N = 527

We find The standard deviation

√p(1-p)/n

√0.07(1-0.07)/527

= √0.0651/527

= 0.01111437889

We are now to get z score

x = 0.09

U = 0.07

Sd = 0.01111437889

Z = x-u/sd

= 0.09-0.07/0.1111437889

= 1.799470775

Going to the statistical table,

P(z>1.799470775)

= 0.035972123

This is in the right tailed area

We approximate to 0.036.