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Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 22.1 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 24.2 in. significantly​ high?

Answer :

Answer:

Step-by-step explanation:

Given that  the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of mu equals 22.1 in. and a standard deviation of sigma equals 1.2 in.

We have to find values of x such that

[tex]P(X\geq a) \leq 0.01\\[/tex] and

[tex]P(X\leq b) \leq 0.01[/tex]

a=2.33 and b =-2.33 as z values

Let us convert to X values

[tex]x=22.1-2.33(1.2) \\x=22.1+2.33(1.2)\\[/tex]

i.e. values below 19.304 and above 25.496

Hence for x below 19.304 and above 25.496 are significantly low and high.

24.2 length is not significantly high.

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