Question

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 613 Americans would differ from the population proportion by greater than 3% ? Round your answer to four decimal places.

Answer 1

sample size = 613

p = 0.07

here we want to find P( | - 0.07 | > 0.03 ) = 1 - P( | - 0.07 | < 0.03 ) = 1 - P( 0.04 < < 0.10 )

= 1 - (P( < 0.10) - P( < 0.04)) ...( 1 )

Mean of sample proportion = 0.07

and standard deviation is as

Let's use excel:

P( < 0.10) = "=NORMDIST(0.1,0.07,0.010305,1)" = 0.9982

P( < 0.04) ="=NORMDIST(0.04,0.07,0.010305,1)" = 0.0018

Plug these values in equation (1 ), we get

P( | - 0.07 | > 0.03 ) = 1 - ( 0.9982 - 0.0018) = 1 - 9964 = 0.0036 (This is the final answer).