Question

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of μ = 24 in. and a standard deviation of sigma equals σ = 1.1 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 26.3 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.

​(Round to one decimal place as​ needed.)

Using these​ criteria, is a​ back-to-knee length of 26.3 in. significantly​ high?

A​ back-to-knee length of 26.3 in. ?(is/is not) significantly high because it is ?(outside/inside) the range of values that are not considered significant.

Answer 1

for 0.01 value at both ends ; critical z=2.33

back-to-knee lengths separating significant values from those that are not significant

=mean-/+ z*std deviation =24-/+2.33*1.1=21.4 ; 26.6

Back-to-knee lengths greater than 21.4 in. and less than 26.6  in. are not​ significant, and values outside that range are considered significant.

A​ back-to-knee length of 26.3 in  is not significantly high because it is inside  the range of values that are not considered significant.