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The heights of adult males in the United States are approximately normally distributed. The mean height is 70 inches (5 feet 10 inches) and the standard deviation is 3 inches.

Use the table to estimate the probability that a randomly -selected male is between 67 and 45 inches tall. Express your answer as a decimal.

The Heights Of Adult Males In The United States Are Approximately Normally Distributed The Mean Height Is 70 Inches 5 Feet 10 Inches And The Standard Deviation class=

Sagot :

Using the normal distribution, it is found that the probability is 0.16.

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, the mean and the standard deviation are given by, respectively, [tex]\mu = 70, \sigma = 3[/tex].

The proportion of students between 45 and 67 inches is the p-value of Z when X = 67 subtracted by the p-value of Z when X = 45, hence:

X = 67:

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

[tex]Z = \frac{67 - 70}{3}[/tex]

Z = -1

Z = -1 has a p-value of 0.16.

X = 45:

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

[tex]Z = \frac{45 - 70}{3}[/tex]

Z = -8.3

Z = -8.3 has a p-value of 0.

0.16 - 0 = 0.16

The probability is 0.16.

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

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