Question

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work​ table, the sitting knee height must be​ considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.1 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.9 in. and a standard deviation of 1.0 in. Use this information to answer the following questions. What is the minimum table clearance required to satisfy the requirement of fitting​ 95% of​ men? nothing in. ​(Round to one decimal place as​ needed.) Determine if the following statement is true or false. If there is clearance for​ 95% of​ males, there will certainly be clearance for all women in the bottom​ 5%. A. The statement is true because some women will have sitting knee heights that are outliers. B. The statement is false because some women will have sitting knee heights that are outliers. C. The statement is true because the 95th percentile for men is greater than the 5th percentile for women. D. The statement is false because the 95th percentile for men is greater than the 5th percentile for women. The author is writing this exercise at a table with a clearance of 23.9 in. above the floor. What percentage of men fit this​ table? nothing​% ​(Round to two decimal places as​ needed.) What percentage of women fit this​ table? nothing​% ​(Round to two decimal places as​ needed.) Does the table appear to be made to fit almost​ everyone? Choose the correct answer below. A. The table will fit only 1​% of men. B. The table will only fit​ 1% of women. C. The table will fit almost everyone except about 1​% of men with the largest sitting knee heights. D. Not enough information to determine if the table appears to be made to fit almost everyone. Click to select your answer(s).

Answer 1

1.

z value for 95th percentile is 1.645

Minimum table clearance required to satisfy the requirement of fitting​ 95% of​ men =

= 21.1 + 1.645 * 1.1 = 22.9 inch

2.

C. The statement is true because the 95th percentile for men is greater than the 5th percentile for women.

3.

z = (x - ) / = (23.9 - 21.1) / 1.1 = 2.55

P(z < 2.55) = 0.9946

percentage of men fit this​ table = 0.9946 * 100 = 99.46 %

z = (x - ) / = (23.9 - 19.9) / 1 = 4

P(z < 4) = 0.99997

percentage of women fit this​ table = 0.99997 * 100 =  99.997 % 100%

The table will fit almost everyone except about 1​% of men with the largest sitting knee heights.