contestada

Automobile manufacturers have to design the driver’s seat area so that both tall and short adults can sit comfortably, reach all the controls and pedals, and see through the windshield. Suppose a new car is designed so that these conditions are met for people from 58 inches to 76 inches tall. The heights of adult men in the United States are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. You can conclude that this design will work for about what % of men?

Respuesta :

Answer:95%

Step-by-step explanation:

Using the normal distribution, it is found that this design will work for about 97.72% of men.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 70, \sigma = 3[/tex].

The proportion of men for which the design works is the p-value of Z when X = 76 subtracted by the p-value of Z when X = 58, hence:

X = 76:

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

[tex]Z = \frac{76 - 70}{3}[/tex]

Z = 2.

Z = 2 has a p-value of 0.9772.

X = 58:

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

[tex]Z = \frac{58 - 70}{3}[/tex]

Z = -4.

Z = -4 has a p-value of 0.

0.9772 - 0 = 0.9772 = 97.72%.

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

#SPJ2

Otras preguntas