Question

A statistician calculates that 9% of Americans are vegetarians. If the statistician is correct, what is the probability that the proportion of vegetarians in a sample of 611 Americans would differ from the population proportion by less than 3%? Round your answer to four decimal places.

Answer 1

P( < A) = P(Z < (A - )/)

= 0.09

n = 611

= = 0.09

=

=

= 0.0116

P(the sample proportion would differ from the population proportion by less than 3%) = P(0.09-0.03 < < 0.09+0.03)

= P(0.06 < < 0.12)

= P( < 0.12) - P( < 0.06)

= P(Z < (0.12 - 0.09)/0.0116) - P(Z < (0.06 - 0.09)/0.0116)

= P(Z < 2.59) - P(Z < -2.59)

= 0.9952 - 0.0048

= 0.9904