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Rzqust [24]
2 years ago
13

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.

Mathematics
1 answer:
steposvetlana [31]2 years ago
3 0

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

<h3>Normal Probability Distribution</h3>

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

Z = \frac{X - \mu}{\sigma}

  • 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, \mu = 70, \sigma = 3.

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

X = 67:

Z = \frac{X - \mu}{\sigma}

Z = \frac{67 - 70}{3}

Z = -1

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

X = 45:

Z = \frac{X - \mu}{\sigma}

Z = \frac{45 - 70}{3}

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 brainly.com/question/24663213

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At a greengrocer, two bananas and one apple cost ?1.16 and one banana and one apple cost ?0.71. How much does one apple cost?
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Find out the how much does one apple cost .

To prove

Let us assume that the number of bananas be x .

Let us assume that the number of apples be y .

As given

At a greengrocer, two bananas and one apple cost $1.16 .

Than the equation becomes

2x + y = 1.16

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Than the equation becomes

x + y = 0.71

Subtracting x + y = 0.71 from 2x + y = 1.16

2x - x + y - y = 1.16 - 0.71

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Put in the equation x + y = 0.71

0.45 + y = 0.71

y = 0.71 - 0.45

y = $0.26

Therefore the cost of the one apple is  $0.26 .


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