# Mathematics homework 1

Question 11.

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 21.6 in. and a standard deviation of 1.2 in. Females have sitting knee heights that are normally distibuted with a mean of 19.4in. and a standard deviation of 1.1 in. Use this information to answer the following questions.

1. What is the minimum table clearance required to satisfy the requirement of fitting 95% of men?

(Round to one decimal place.)

2. Determine if the following statement is true or false. If there is clearance for 95% of males, there wil certainly be clearance for all women in the bottom 5%. (Choices)

a. False, bc the 95th percentile for men is greater than the 5th percentile for women

b. True, because the 95th percentile for men is greater than the 5th percentile for women

c. False, bc some women wil have sitting knee heights that are outliers

d. True, bc some women will have sitting knee heights that are outliers

3. The author is writing this exercise at a table with a clearance of 23.9in above the floor. What percentage of men fit this table? (round to 2 decimal places)

4. What percenage of women fit this table? (round to 2 decimal plces)

5. Does it appear this table will fit everyone? (choices)

a. only 1% of women

b. only 3% of men

c. almost everyone except about 3% of men with largest sitting knee heights

d. not enough info to determine

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