Using the Central Limit Theorem. In Exercises use this information about the overhead reach distances of adult females:μ = 205.5 cm,σ = 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.

a. If 1 adult female is randomly selected, find the probability that her overhead reach is greater than 218.4 cm.

b. If 9 adult females are randomly selected, find the probability that they have a mean overhead reach greater than 204.0 cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Answer:

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The overhead reach distances of adult females = 205.5 cm and = 8.6 cm and overhead reach distances are normally distributed. The overhead reach distances are used in planning assembly work stations.

a. If 1 adult female is randomly selected, the probability that her overhead reach is greater than 218.4 cm.

We are dealing with individual value from a normally distributed population so mean is 205.5 cm and standard deviation is 8.6 cm.

The Test Statistic can be expressed as

Z = 1.5

To find the associated probability, we have

P()

P(Z > 1.5) = 1 - P(Z 1.5)

= 1 - 0.9332 (From Area Under Normal Curve table)

= 0.0668