A common design requirement is that an environment must fit the range of people who fall between the $5^{\text {th }}$ percentile for women and the $95^{\text {th }}$ percentile for men. In designing an assembly work th 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 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? in, (Round to one decimal place as needed.)

Step 1 ：The problem is asking for the minimum table clearance required to satisfy the requirement of fitting 95% of men. This means we need to find the sitting knee height at the 95th percentile for men.

Step 2 ：Since the sitting knee heights are normally distributed, we can use the z-score formula to find this value. The z-score formula is \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the value we're looking for, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 3 ：In this case, we know the z-score corresponding to the 95th percentile (from a standard normal distribution table or using a statistical function), and we need to solve for \(X\). Rearranging the formula gives us \(X = Z\sigma + \mu\).

Step 4 ：Given that the mean sitting knee height for men (\(\mu\)) is 21 inches, the standard deviation (\(\sigma\)) is 1.2 inches, and the z-score for the 95th percentile (\(Z\)) is approximately 1.645, we can substitute these values into the formula to find \(X\).

Step 5 ：Doing so gives us \(X = 1.645 \times 1.2 + 21\), which simplifies to approximately 22.97 inches.

Step 6 ：This means that 95% of men have a sitting knee height of 22.97 inches or less. Therefore, to satisfy the requirement of fitting 95% of men, the minimum table clearance required would be this value.

Step 7 ：Final Answer: The minimum table clearance required to satisfy the requirement of fitting 95% of men is approximately \(\boxed{22.97}\) inches.