Question

A common design requirement is that an environment must fit the range of people who fall between the 5thpercentile 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 heightsthat are normally distributed with a mean of 21.5 in. and a standard deviation of 1.3 in. Females have sitting knee heights that are normally distributed with a mean of 19.1 in. and a standard deviation of 1.2 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?

Answer 1

First, we need to find the z-value for a probability of 95%.

Looking at the z-table, for p = 0.95 we have z = 1.645.

Then, to find the table clearance, we can use the formula below:

`z=(x-\mu)/(\sigma)`

Since the mean is equal to 21.5 inches and the standard deviation is equal to 1.3 inches, we have:

`\begin{gathered} 1.645=(x-21.5)/(1.3) \\ x-21.5=1.645\cdot1.3 \\ x-21.5=2.14 \\ x=2.14+21.5 \\ x=23.64\text{ inches} \end{gathered}`

Rounding to one decimal place, we have x = 23.6 inches.