Directions: Round areas or probability values to 4 decimal places. Round z value

Question

Directions:

Round areas or probability values to 4 decimal places.

Round z values to 2 decimal places before using these for other computations.

A. Normal Distributions

1. Designing Cars. The sitting height (from seat to top of head) of drivers must be considered in the design of a new car model. Men have sitting heights that are normally distributed with a mean of 36.0 inches and a standard deviation of 1.4 inches (based on anthropometric survey data from Gordon, Clauser, et al). Engineers have provided plans that can accommodate men with sitting heights up to 38.8 heights, but taller men cannot fit. If a man is randomly selected, find the probability that he has a sitting height less than 38.8 inches.  

Explanation / Answer

Solution;- mean = 36, sd = 1.4

= > P( X < 38.8) = P( Z < (38.8-36)/1.4)

= P( Z < 2)

= 0.9772

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