Problema Solution
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 in. and a standard deviation of 1.4 in.
a) One car is designed to accommodate sitting heights of 38.8 in. or less. Fine the percentage of men with sitting heights greater than 38.8 in.
b) If the sitting height is to be changed so that 98% of men will be accommodated, what is the new sitting height?
Answer provided by our tutors
a) One car is designed to accommodate sitting heights of 38.8 in. or less. Fine the percentage of men with sitting heights greater than 38.8 in
P(X > 38.8) = 1 - P(X < 38.8) = 1 - P(z<(38.8 - 36.0)/1.4) = 1 - P(z < 2.0) = 1 - 0.9972 = 0.0028 or 0.28%