Question

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of μ=24.0 in. and a standard deviation of 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 _____ nothing in. are not​ significant, and values outside that range are considered significant.

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

***A​ back-to-knee length of 25.3 in. ______ [is or is not] significantly high because it is _______ [Inside or outside] the range of values that are not considered significant.

Answer 1

Answer:

Given that,

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of μ=24.0 in.

And a standard deviation of σ=1.1 in.

Insignificant values are :

P( x or greater )   0.01 and P( x or less ) 0.01

P( x or greater ):

Let the value be x_g

To obtain cut off assume

P( ( x -μ )/σ    ( x_g - μ)/σ) = 0.01

P( ( x -24.0 )/1.1    ( x_g - 24.0)/1.1) = 0.01

......................(1)

..........................(2)

Comparing (1) and (2)

P(x or less):

Let the value be x_i

To obtain cut off assume

............................(1)

......................(2)

Comparing (1) and (2)

Back to knee length greater than 26.56 in. and less than 22.44 in. are not significant, and values outside that range are considered significant.

Therefore, A​ back-to-knee length of 2.63 in. is not significantly high because it is outside the range of values that are not considered significant.