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. Answer parts​ (a) through​ (d).

b. What is the probability that in the sample between 36​% and 47​% say that having a flexible work schedule is either very important or extremely important to their career​ success?

Answer 1

Solution:

Given: 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.

That is: p = proportion of f women saying that having a flexible work schedule is either very important or extremely important to their career success = 41%

thus p = 0.41

Sample size = n = 100

Part b) What is the probability that in the sample between 36​% and 47​% say that having a flexible work schedule is either very important or extremely important to their career​ success?

That is we have to find:

Since sample size = n = 100 is large and thus we can use Normal approximation to proportion if following assumptions are satisfied:

Thus

and

Thus we can use Normal approximation to proportion .

Find z scores:

and

Thus we get:

Look in z table for z = -1.0 and 0.02 as well as for z = 1.2 and 0.02 and find corresponding area.

Thus we get:

P( Z < -1.02) = 0.1539

P( Z < 1.22) =0.8888

Thus we get:

Thus the probability that in the sample between 36​% and 47​% say that having a flexible work schedule is either very important or extremely important to their career​ success is 0.7349