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 42% 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 34% and 49% say that having a flexible work schedule is either very important or extremely important to their career success?

Answer 1

Solution

Given that,

p = 42% = 0.42

1 - p = 1 - 0.42 = 0.58

n = 100

= p = 0.42

=  [p ( 1 - p ) / n] = [(0.42 * 0.58) / 100 ] = 0.0494

P( 0.34 < < 0.49 )

= P[(0.34 - 0.42) / 0.0494 < ( - ) / < (0.49 - 0.42) / 0.0494]

= P( -1.62 < z < 1.42)

= P(z < 1.42) - P(z < -1.62)

Using z table,   

= 0.9222 - 0.0526

= 0.8696