American Special Forces: A primary requirement for acceptance into American Spec

Question

American Special Forces:

A primary requirement for acceptance into American Special Forces is to have an IQ score above 120. Twenty candidates take IQ tests, and their summary results indicated that their mean IQ score is 124. (IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.)

If 1 person is randomly selected from the general population, find the probability of getting someone with and IQ of at least 124.

If 20 people are randomly selected, find the probability that their mean IQ score is at least 124.

Although the summary results are available, the individual IQ scores have been lost. Can it be concluded that all 20 candidates have IQ scores above 120 so that they are all eligible for American Special Forces.

Using the Central Limit Theorem. In exercises 2 and 3, use this information about the overhead reach distances of adult females: µ = 205.5 cm, = 8.6 cm, and overhead reach distances are normally distributed (based on data from the Federal Aviation Administration). The overhead reach distances are used in planning assembly work stations.

If 1 adult female is randomly selected, find the probability that her overhead reach is between 179.7 cm and 231.3 cm.

If 40 adult females are randomly selected, find the probability that they have a mean overhead reach between 204.0 cm and 206.0 cm.

Explanation / Answer

(a) = 120, = 15, x = 124

z = (124 - 120)/15 = 0.2667

P(x 124) = P(z > 0.2667) = 0.3949

(b) = 120, = 15, x-bar = 124, n = 20

z = (124 - 120)/(15/20) = 1.1926

P(x-bar 124) = P(z > 1.1926) = 0.1165

(c) No, such a conclusion cannot be drawn.

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