Answer to Question #150590 in Statistics and Probability for Vladimyr Lubin

Question

(6.2.19) Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu=23.6 in. and a standard deviation of alpha=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)</=0.01 and a value is significantly low if​ P(x or ​less)</=0.01. 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 26.0 in. significantly​ high?
Find the​ back-to-knee lengths separating significant values from those that are not significant.
​Back-to-knee lengths greater than ? in. and less than ? in. are not​ significant, and values outside that range are considered significant.

Answer 1

$Lower = \mu - Z_{0.99}*\sigma = 23.6 - 2.3263*1.2 = 20.8\\ Upper = \mu + Z_{0.99}*\sigma = 23.6 + 2.3263*1.2 = 26.4$

A​ back-to-knee length of 26.0 in. is not significantly high because it is

inside the range of values that are not considered significant.