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.

d. If a sample of 400 is​ taken

The probability that in the sample fewer than 48​% say that having a flexible work schedule is either very important or extremely important to their career success 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 is

The probability that in the sample more than 42% say that having a flexible work schedule is either very important or extremely important to their career success is

Answer 1

Solution

Given that,

p = 0.41

1 - p = 1 - 0.41 = 0.59

n = 400

= p = 0.41

=  [p ( 1 - p ) / n] =   [(0.41 * 0.59) / 400 ] = 0.0246

a) P( < 0.48)

= P[( - ) / < (0.48 - 0.41) / 0.0246 ]

= P(z < 2.85)

Using z table,

= 0.9978

b) P( 0.33 < < 0.48)

= P[(0.33 - 0.41) / 0.0246 < ( - ) / < (0.48 - 0.41) / 0.0246 ]

= P(-3.25 < z < 2.85)

= P(z < 2.85) - P(z < -3.25)

Using z table,   

= 0.9978 - 0.0006

= 0.9972

c) P( > 0.42) = 1 - P( < 0.42)

= 1 - P(( - ) / < (0.42 - 0.41) / 0.0246)

= 1 - P(z < 0.41)

Using z table

= 1 - 0.6591

= 0.3409