Question

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 23.4 in. and a standard deviation of sigma equals 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)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 25.7 in. significantly​ high?

Answer 1

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 23.4 in. and a standard deviation of sigma equals 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)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 25.7 in. significantly​ high?

Z values for top and bottom 0.01 level or 1% level is 2.326 and -2.326

The lower value = mean+z*sd = 23.4-2.326*1.1 = 20.8414

The upper value = mean+z*sd = 23.4+2.326*1.1 = 25.9586

The two lengths separating significant values are ( 20.84 and 25.96)

The value 25.7 is lower than the high value 25.96.

Therefore back-to-knee length of 25.7 in. is not significantly​ high.