Question

I ONLY NEED PART D Thank you

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 100 working women. Answer parts​ (a) through​ (d).

a. What is 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?

. 9463

(Round to four decimal places as​ needed.)b. What 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?

. 7344

​(Round to four decimal places as​ needed.)c. What 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?

. 3446

PART D. ​(Round to four decimal places as​ needed.)d. If a sample of 400 is​ taken, how does this change your answers to​ (a) through​ (c)?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

a)
Here, μ = 0.45, σ = 0.0249 and x = 0.53. We need to compute P(X <= 0.53). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (0.53 - 0.45)/0.0249 = 3.21

Therefore,
P(X <= 0.53) = P(z <= (0.53 - 0.45)/0.0249)
= P(z <= 3.21)
= 0.9993

b)
Here, μ = 0.45, σ = 0.0249, x1 = 0.41 and x2 = 0.53. We need to compute P(0.41<= X <= 0.53). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (0.41 - 0.45)/0.0249 = -1.61
z2 = (0.53 - 0.45)/0.0249 = 3.21

Therefore, we get
P(0.41 <= X <= 0.53) = P((0.53 - 0.45)/0.0249) <= z <= (0.53 - 0.45)/0.0249)
= P(-1.61 <= z <= 3.21) = P(z <= 3.21) - P(z <= -1.61)
= 0.9993 - 0.0537
= 0.9456

c)

Here, μ = 0.45, σ = 0.0249 and x = 0.47. We need to compute P(X >= 0.47). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (0.47 - 0.45)/0.0249 = 0.8

Therefore,
P(X >= 0.47) = P(z <= (0.47 - 0.45)/0.0249)
= P(z >= 0.8)
= 1 - 0.7881 = 0.2119