Suppose that the sitting back-to-knee length for a group of adults has a normal

Question

Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of -247/n and a standard deviation of = 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) s 0.01 and a value is significantly low if P(x or less)s 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 27.1 in significantly high? Find the back-to-knee lengths separating significant values from those that are not significant. Back-to-knee lengths greater than O in. and less than 0 in. are not significant, and values outside that range are considered significant. (Round to one decimal place as needed.) Enter your answer in each of the answer boxes. Save for Later 636 AM 2419/2018 0 Type here to search

Explanation / Answer

Ans:

Given that

mean=24.7

standard deviation=1.2

P(Z<=z)=0.01

z=-2.33

lower limit=24.7-2.33*1.2=21.9

P(Z>=z)=0.01

P(Z<=z)=1-0.01=0.99

z=2.33

upper limit=24.7+2.33*1.2=27.5

Greater than 27.5 and less than 21.9 are not significant.

As,27.1 is not in the range of significantly high(if x>27.5,then significantly high).

A back to knee length of 27.1 is not significantly high,because it is inside the range of values that are not significantly high or low.

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