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?

Question

25-02-2022
Mathematics

contestada

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 :

Otras preguntas

(100 points boys) Just this one question for my math.

A 12 kg barrel is pulled up by a rope. The barrel accelerates at 1.2 m/s2. Find the force exerted by the rope. Show all your work.

What does self-governance mean?

For a representative farm before the study, the economic loss is equal to A. the price multiplied by the quantity produced. B. the difference in price and l

The Clydesdale Company has sales of $4,500,000. It also has invested assets of $2,000,000 and operating expenses of $3,600,000. The company has established a mi

Which is the correct description of chasquis? A) trained runners who carried news throughout the Inca Empire B) clan groups used for taxation in the Inca

Clayton does well at work. He his strong, productive relationships with co-workers and is motivated to achieve and get promotions. He often does well more than

On January 1, Weatherholt Inc. issued $5,000,000, 9% bonds for $4,695,000. The market rate for these bonds is 10%. Interest is payable annually on December 31.

Lana Reid is an accounting clerk at Tenity Enterprises who is paid $18.15 per hour. During a week’s pay period, she worked 39 hours and 41 minutes. Based on a h

In training for a swim meet, Logan swam 750 meters in 1/3 of an hour. His swimming partner , swam 2/3 of Logan’s distance in 1/4 of an hour

joaobezerra joaobezerra · Answer 1 · 2022-03-02T11:03:59+01:00

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