Answer to Question #210566 in Statistics and Probability for belle

Question

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of

μ=23.9

in. and a standard deviation of

σ=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

26.1

in. significantly​ high?

Find the​ back-to-knee lengths separating significant values from those that are not significant.

​Back-to-knee lengths greater than 

Answer 1

$Lower = \mu-z_{0.99}\times\sigma$

$=23.9-(2.32635\times1.2)=21.1$

$Upper = \mu+z_{0.99}\times\sigma$

$=23.9+(2.32635\times1.2)=26.7$

Since 26.1 falls within the interval {21.1,26.7}, it is not significantly high.