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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 21.8 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 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 requirements of fitting 95% of men?

Respuesta :

Using the normal distribution, it is found that the minimum table clearance required to satisfy the requirements of fitting 95% of men is of 23.6 in.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, for men's knee heights, we have that:

  • The mean is of [tex]\mu = 21.8[/tex].
  • The standard deviation is of [tex]\sigma = 1.1[/tex].

The 95th percentile is X when Z has a p-value of 0.95, so X when Z = 1.645, then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 21.8}{1.1}[/tex]

[tex]X - 21.8 = 1.1(1.645)[/tex]

[tex]X = 23.6[/tex]

The minimum table clearance required to satisfy the requirements of fitting 95% of men is of 23.6 in.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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