Question

# 1. Assume that adults have IQ scores that are normally distributed with a mean of 104.3...

1. Assume that adults have IQ scores that are normally distributed with a mean of 104.3 and a standard deviation of 23.8. Find the probability that a randomly selected adult has an IQ greater than 147.0. The probability that a randomly selected adult from this group has an IQ greater than 147.0 is..

2. Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90​% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.8  in. and a standard deviation of 0.9 in. Find UpperP90. That​ is, find the hip breadth for men that separates the smallest 90​% from the largest 10​%.

The hip breadth for men that The hip breadth for men that separates the smallest 90​% from the largest 10​% is P90= in.

3. Assume that adults have IQ scores that are normally distributed with a mean of 101.4 and a standard deviation17.

Find the first quartile Upper Q1​, which is the IQ score separating the bottom​ 25% from the top​ 75%.

4. Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of μ=24.9 in. and a standard deviation of σ=1.1in. 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 27.0 in. significantly​ high?

​Back-to-knee lengths greater than...in. and less than.. in. are not​ significant, and values outside that range are considered significant. ​(Round to one decimal place as​ needed.)

** PS: I have rounded all the four answers to four decimal places. Please round them as per your requirement. Thank you......

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