Question

A statistician calculates that 7% of Americans are vegetarians. If the statistician is correct, what is the probability that the proportion of vegetarians in a sample of 883 Americans would be greater than 5%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 7%=0.07

1 - p = 1-0.07=0.93

n = 883

= p =0.07

=  [p( 1 - p ) / n] = [(0.07*0.93) / 883 ] = 0.009

P( > 0.05) = 1 - P( <0.05 )

= 1 - P(( - ) / < (0.05-0.07) /0.009 )

= 1 - P(z <-2.22 )

Using z table

= 1 -0.0132

=0.9868

probability=0.9868