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 21.7 in. and a standard deviation of 1.2 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 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? 23.7 in.

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? 95.25​%

What percentage of women fit this​ table?

Answer 1

Solution:-

Given that,

mean = = 19.3 in.

standard deviation = = 1.1 in.

Using standard normal table,

P(Z < z) = 5%

= P(Z < z ) = 0.05

= P(Z < -1.645 ) = 0.05  

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 1.1 + 19.3

x = 17.5 in.

17.5 in. the minimum table clearance required to satisfy the requirement of fitting​ 5% of​ women

P(x < 17.5) = P[(x - ) / < (17.5 - 19.3) / 1.1]

= P(z < -1.64)

Using z table,

= 0.0505

The percentage is = 5.05%