Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 23.3 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 25.6 in. significantly high?

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mtosi17 mtosi17 · Answer 1 · 2020-07-11T02:56:42+02:00

Answer:

The back-to-knee lengths separating significant values from those that are not significant are 20.2 in. and 26.4 in.

Using these criteria, a back-to-knee length of 25.6 in. is not significantly high, as is within the not-significant values.

Step-by-step explanation:

We have a normal distribution for the sitting back-to-knee length with mean 23.3 in. and standard deviation 1.2 in.

We have to calculate the critical values that limit the 1% right tail and 1% left tail.

This can be done looking for a standard normal distribution table for the values that satisfy:

[tex]P(z>z^*)=0.01\;\;\;\text{(for the right tail)}\\\\P(z<-z^*)=0.01\;\;\;\text{(for the left tail)}[/tex]

This values for z are z=±2.576.

Then, we can calculate the bounds for our sitting back-to-knee length distribution as:

[tex]X_1=\mu+z_1\cdot\sigma=23.3+(-2.597)\cdot 1.2=23.3-3.1=20.2\\\\ X_2=\mu+z_2\cdot\sigma=23.3+(2.597)\cdot 1.2=23.3+3.1=26.4[/tex]