Question

A sample survey interviews an simple random sample of 259 college women. Suppose (as is roughly true) that 68% of all college women have been on a diet within the past 12 months. What is the probability that 74% or more of these women in the sample have been on a diet (round answer to four decimal places. Notice that you may need to carry 3 or more significant digits for any intermediate calculations.

Answer 1

Sample size, n = 259

Population proportion, p = 0.68

For sampling proportion ,

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

= = 0.68

=

=

= 0.029

P(74% or more of these women in the sample have been on a diet) = P( > 0.74)

= 1 - P( < 0.74)

= 1 - P(Z < (0.74 - 0.68)/0.029)

= 1 - P(Z < 2.07)

= 1 - 0.9808

= 0.0192