Question

A global research study found that the majority of today's working women would prefer a better work-life balance to an increased salary. One of the most important contributors to work-life balance identified by the survey was "flexibility," with 41% of women saying that having a flexible work schedule is either very important or extremely important to their career success. Suppose you select a sample of 100 working women.

What is the probability that in the sample between 33% and 48% say that having a flexible work schedule is either very important or extremely important to their career success?

Answer 1

Using normal approximation,

P( < p ) = P(Z < ( - p) / sqrt [ p ( 1 - p) / n ]

So,

P(0.33 < < 0.48) = P( < 0.48) - P( < 0.33)

= P(Z < ( 0.48 - 0.41) / sqrt [ 0.41 ( 1 - 0.41) / 100] - P(Z < ( 0.33 - 0.41) / sqrt [ 0.41 ( 1 - 0.41) / 100]

= P(Z < 1.42) - P(Z < -1.63)

= P(Z < 1.42) - ( 1 - P(Z < 1.63) )

= 0.9222 - ( 1 - 0.9484 ) (From Z table)

= 0.8706