Question

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 22.7 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 24.9 in. significantly​ high? Find the​ back-to-knee lengths separating significant values from those that are not significant. ​Back-to-knee lengths greater than nothing in. and less than nothing in. are not​ significant, and values outside that range are considered significant. ​(Round to one decimal place as​ needed.).

Answer 1

µ =    22.7                      
σ =    1.2                     
z value at   0.01   = ±   2.326   (excel formula =NORMSINV(   0.02   / 2 ) )  
                          
z = ( x - µ ) / σ                          
so, X = z σ + µ =                          
X1 =   -2.326   *   1.2   +   22.7   =   19.9
X2 =   2.326   *   1.2   +   22.7   =   25.5

​Back-to-knee lengths greater than 25.5

. and less than 19.9  are not​ significant,

24.9 in. is not significantly high

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