To be eligible for a certain job, women must be at least 62 inches tall, and 87% of women meet this criterion. In a random sample of 2000 women, X = number who qualify for the job (based on height)....

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To be eligible for a certain job, women must be at least 62 inches tall, and 87% of women meet this criterion. In a random sample of 2000 women, X = number who qualify for the job (based on height).

a. Use the normal curve to approximate P(X ≤ 1700), the probability that 1700 or fewer women have the necessary height to qualify for the job.

b. Use statistical software, Excel, or a graphing calculator to find the exact binomial probability that 1700 or fewer women in the sample are tall enough to qualify for the job.

Answered Same DayDec 25, 2021

Answer To: To be eligible for a certain job, women must be at least 62 inches tall, and 87% of women meet this...

Robert answered on Dec 25 2021

122 Votes

transtutors.com/questions/-2131041.htm
in
X ∼ Binomial(n = 2000, p = 0.87)
Binomial can be approximated to normal with:
µ = np = 2000 ∗ 0.87 = 1740
σ =
√
np(1 − p) =
√
2000 ∗ (0.87)(1 − 0.87) = 15.039947 ≈ 15.040
P (X ≤ 1700)
Since we are approximating a discrete distribution by continuous normal dis-
tribution, values between 1699.5 and 1700.5 both approximate to 1700. Thus,
“less than or equal to 1700 ” corresponds to continuous normal distribution with
X < 1700.5 after continuity correction.
Normal...

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To be eligible for a certain job, women must be at least 62 inches tall, and 87% of women meet this criterion. In a random sample of 2000 women, X = number who qualify for the job (based on height)....

Answer To: To be eligible for a certain job, women must be at least 62 inches tall, and 87% of women meet this...

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