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 foot to the top of the knee. males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.2 in. females have sitting knee heights that are normally distributed with a mean of 19.1 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? in (round to one decimal place as needed.)

Explanation:

Step1: Find the z - score for the 95th percentile

The 95th percentile corresponds to a cumulative probability of 0.95. Looking up in the standard normal distribution table (z - table), the z - score $z$ such that $P(Z\leq z)=0.95$ is approximately $z = 1.645$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the original normal distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to find $x$ (sitting knee height for men), $\mu = 21.4$ in and $\sigma=1.2$ in.
We can re - arrange the formula to solve for $x$: $x=\mu + z\sigma$.

Step3: Substitute the values

Substitute $\mu = 21.4$, $z = 1.645$, and $\sigma = 1.2$ into the formula:
$x=21.4+1.645\times1.2$.
First, calculate $1.645\times1.2 = 1.974$.
Then, $x=21.4 + 1.974=23.374\approx23.4$ in.

Answer:

23.4