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

21.5

in. and a standard deviation of

1.2

in. Females have sitting knee heights that are normally distributed with a mean of

19.2

in. and a standard deviation of

1.1

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 false because some women will have sitting knee heights that are outliers.

B.

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

C.

The statement is true because some women will have sitting knee heights that are outliers.

D.

The statement is true 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

23.7

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

33​%

of men.

B.The table will fit almost everyone except about

33​%

of men with the largest sitting knee heights.

C.

The table will only fit​ 1% of women.

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

a)

Let the random variable X be the sitting knee height of men and it follows normal distribution with mean μM=21.5 and standard deviation σM=1.2 inches.

Let the random variable Y be the sitting knee height of women and it follows normal distribution with mean μF=19.2 and standard deviation σF​=1.1 inches.

The minimum table clearance required to satisfy the requirement of fitting 95% of men is,

The minimum table clearance required to satisfy the requirement is 23.4 inches.

Explanation

From the standard normal table, the value of z score at 0.95 is 1.645. Using the value, the minimum table clearance is obtained at 23.4 inches.

b)

If there is clearance for 95% of males, there will certainly be clearance for all women in the bottom 5%.

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

Explanation

The statement is true as it is given that the common design must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men.