A common design requirement is that an environment must fit the range of people

Question

A common design requirement is that an environment must fit the range of people who fall between the 5^th percentile for women and the 95^th 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 normal distributed with a mean of 21.6 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? ____________ in. 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 false because the 95th percentile for men is greater than the 5th percentile for women. 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 23.8 in. above the floor what percentage of men fit this table? ___________ % What percentage of women fit this table? ___________ % Does the table appear to be made to everyone? Choose the correct answer below. A. The table will fit almost everyone except about 2% of men with the largest sitting knee heights. B. The table will fit only 2% of men. 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.

Explanation / Answer

For Men, mean = 21.6 and std. dev. = 1.1
For Women, mean = 19.9 and std. dev. = 1

For 95%, z-value = 1.64
As per given condition, clearance height of men at 95% percentile would be
xbar = mean + z*sigma
xbar = 21.6 + 1.64*1.1
xbar = 23.404

Lets find the clearance height required for bottom 5% women, z-value = -1.64
xbar = mean + z*sigma
xbar = 19.9 - 1.64*1
xbar = 18.26

As bottom 5% value for women is less than top 95% of men, given statement is true.
Option D is correct.

Lets find probability that men height will be less than 23.8 in.
P(X<23.8) = P(z<(23.8-21.6)/1.1) = P(z<2) = 0.9772
Hence 97.72% of men will fit.

Lets find the probability that women height will be less than 23.8 in
P(X<23.8) = P(z<(23.8-19.9)/1) = P(z<3.9) = 0.99995
Hence 99.995% (100%) of women will fit.

The table will fit almost everyone except about 2% of men with the largest sitting knee heights.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.