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 45​% 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 400 working women.

The probability that in the sample fewer than 53​% 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 41​% and 53​% 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 47​% say that having a flexible work schedule is either very important or extremely important to their career success is

Answer 1

Solution:

Given ,

p = 0.45 (population proportion)

1 - p = 1 - 0.45 = 0.55

n = 400 (sample size)

Let be the sample proportion.

he sampling distribution of is approximately normal with

mean = =  p = 0.45

SD = =     

=  

=  0.02487468592

a)Find P(Sample proportion is less than 53%)

= P( < 0.53)

=

=  P(Z <(0.53-0.45)/ 0.02487468592 )

= P(Z < 3.216)

=  0.9994 ...use z table

P(Sample proportion is less than 53%) = 0.9994

b) Find P(Sample proportion is between 41% and 53%)

= P(0.41 < < 0.53)

= P( < 0.53) - P( < 0.41)

= -

= P(Z <(0.53-0.45)/ 0.02487468592 ) - P(Z <(0.41-0.45)/ 0.02487468592 )

= P(Z < 3.216) - P(Z < -1.608)

= 0.9994 - 0.0539

= 0.9455

P(Sample proportion is between 41% and 53%) = 0.9455

c)

P(Sample proportion is more than 47%)

= P( > 0.47)

=

=  P(Z > (0.47-0.45)/ 0.02487468592 )

= P(Z > 0.804)

= P(Z < -0.804)

= 0.2107

P(Sample proportion is more than 47%) = 0.2107