A. Normal Distributions 1. Designing Cars . The sitting height (from seat to top
ID: 3128229 • Letter: A
Question
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.
2. A company that has a large number of supermarket grocery stores claims that customers who pay by personal checks spend an average of $87 on groceries at these stores with a standard deviation of $22. Assume that the expenses incurred on groceries by all such customers at these stores are normally distributed.
a) Find the probability that a randomly selected customer who pays by check spends more than $114 on groceries.
b) What percentage of customers paying by check spend between $40 and $60 on groceries?
c) What percentage of customers paying by check spend between $70 and $105?
d) Is it possible for a customer paying by check to spend more than $185? Explain.
Explanation / Answer
1.
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 38.8
u = mean = 36
s = standard deviation = 1.4
Thus,
z = (x - u) / s = 2
Thus, using a table/technology, the left tailed area of this is
P(z < 2 ) = 0.977249868 [ANSWER]
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