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 less than 222.7 cm.

b. If 49 adult females are randomly selected, find the probability that they have a mean overhead reach less than 207.0 cm.

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 less than 222.7 cm is:

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 = 2

To find the associated probability, we have

P()

P(Z 2) = 0.9772 (From Area Under Normal Curve table)