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 49​% 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 46​% and 54​% say that having a flexible work schedule is either very important or extremely important to their career​ success?

Answer 1

Given, P = 0.49 and n = 100

the probability that in the sample between 46​% and 54​% say that having a flexible work schedule is either very important or extremely important to their career​ success

P1^ = 0.46 and P2^ = 0.54

Z = (P^-P)/SQRT(P(1-P)/n)

P(0.46 < P^ < 0.54) = P((0.46-0.49)/SQRT(0.49(1-0.49)/100) < Z < (0.54-0.49)/SQRT(0.49(1-0.49)/100))

= P(-0.6 < Z < 1)

= P(Z < 1) - P(Z < -0.6) = 0.8413-0.2743 = 0.567

P(0.46 < P^ < 0.54) = 0.5670