Question

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 24.8 in. and a standard deviation of sigma equals 1.2 in. These data are often used in the design of different​ seats, including aircraft​ seats, train​ seats, theater​ seats, and classroom seats. Instead of using 0.05 for identifying significant​ values, use the criteria that a value x is significantly high if​ P(x or ​greater)less than or equals0.01 and a value is significantly low if​ P(x or ​less)less than or equals0.01. Find the​ back-to-knee lengths separating significant values from those that are not significant. Using these​ criteria, is a​ back-to-knee length of 27.0 in. significantly​ high?

Answer 1

z score for 0.01 area in the right tail = 2.33

z score for 0.01 area in the left = -2.33

Hence,

Interval seperating significant values from those that are not significant is:

(24.8 - 2.33*1.2, 24.8 + 2.33*1.2)

(22.00, 27.60)

This is not significantly high because it is between the above interval values.