A global research study found that the majority of today\'s working women would

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 46% 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). a. What is the probability that in the sample fewer than 54% say that having a flexible work schedule is either very important or extremely important to their career success? 0.9458 (Round to four decimal places as needed.) b. What is the probability that in the sample between 43% and 54% say that having a flexible work schedule is either very important or extremely important to their career success? (Round to four decimal places as needed.)

Explanation / Answer

Here, we have to calculate the probability that less than 54% want flexible work schedule

so here we will find first standard error of the proportions se0 = sqrt [p(1-p)/n] = sqrt [0.46 * 0.54/100] = 0.0498

(a) Pr ( p < 0.54; 0.46 ; 0.0498) = ?

Z = ( 0.54 - 0.46)/ (0.0498) = 1.6064

Pr ( p < 0.54; 0.46 ; 0.0498) = (1.6) = 0.9452

where is the cumulative normal probability distribution.

b. Pr( 0.43 < p < 0.54; 0.46 ; 0.0498) = Pr( p < 0.54; 0.46 ; 0.0498) - Pr( p < 0.43; 0.46 ; 0.0498)

Z values for p = 0.54 and p = 0.43 are

Z1 = (0.43- 0.46)/ 0.0498 = -0.6024

So Pr( 0.43 < p < 0.54; 0.46 ; 0.0498) = (1.6) - (-0.6) = 0.9452 - 0.2743 = 0.6709

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