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 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 100 100 working women. Answer parts​ (a) through​ (d). a. What is the probability that in the sample fewer than 50 50​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.) b. What is the probability that in the sample between 35 35​% and 50 50​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.) c. What is the probability that in the sample more than 43 43​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.) d. If a sample of 400 400 is​ taken, how does this change your answers to​ (a) through​ (c)? The probability that in the sample fewer than 50 50​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing . The probability that in the sample between 35 35​% and 50 50​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing . The probability that in the sample more than 43 43​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing .

Answer 1

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 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. Answer parts​ (a) through​ (d).

42% is proportion of p=0.42

Binomial distribution used n=100, p=0.42

Standard error =sqrt( pq/n) =sqrt(0.42*0.58/100) =0.0494

a. What is the probability that in the sample fewer than 50​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.)

z value for 0.5, z =(0.5-0.42)/0.0494 = 1.62

P( p < 0.5) = P( z < 1.62)

=0.9474

b. What is the probability that in the sample between 35​% and 50​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.)

z value for 0.35, z =(0.35-0.42)/0.0494 = -1.42

z value for 0.5, z =(0.5-0.42)/0.0494 = 1.62

P( 0.35<p<0.5) = P( -1.42<z<1.62)= P( z < 1.62)-P( z < -1.42)

=0.9474- 0.0778

=0.8696

c. What is the probability that in the sample more than 43​% say that having a flexible work schedule is either very important or extremely important to their career​ success? nothing ​(Round to four decimal places as​ needed.)

z value for 0.43, z =(0.43-0.42)/0.0494 = 0.20

P( p >0.43) = P( z > 0.20)

= 0.4207

d. If a sample of 400 is​ taken, how does this change your answers to​ (a) through​ (c)?

Binomial distribution used n=400, p=0.42

Standard error =sqrt( pq/n) =sqrt(0.42*0.58/400) =0.0247

The probability that in the sample fewer than 50​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing .

z value for 0.5, z =(0.5-0.42)/0.0247= 3.24

P( p < 0.5) = P( z < 3.24)

= 0.9994

The probability that in the sample between 35​% and 50​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing .

z value for 0.35, z =(0.35-0.42)/0.0247= -2.84

P( 0.35<p<0.5) = P( -2.84<z<3.24)= P( z < 3.24)-P( z < -2.84)

=0.9994- 0.0023

=0.9971

The probability that in the sample more than 43​% say that having a flexible work schedule is either very important or extremely important to their career success is nothing .

z value for 0.43, z =(0.43-0.42)/0.0247 = 0.41

P( p >0.43) = P( z > 0.41)

= 0.3409