How to find the middle 80 of a normal distribution

Asked by admin @ in Mathematics viewed by 380 People

The distribution of heights for adult men in a certain population is approximately normal with mean 70 inches and standard deviation 4 inches. Which of the following represents the middle 80 percent of the heights?

A) 50 inches to 73.37 inches
B) 62 inches to 78 inches
C) 64.87 inches to 75.13 inches
D) 66 inches to 74 inches
E) 66.63 inches to 90 inches

Answered by admin @


The height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches and this can be determined by using the given data.

Given :

The distribution of heights for adult men in a certain population is approximately normal with a mean of 70 inches and a standard deviation of 4 inches.

The heights that represent the middle 80 percent of the heights are:

\rm P(x_1

\rm P(\dfrac{x_1-\mu}{\sigma}

P(-z < Z < z) = 0.80

P(Z < z) - P(Z < -z) = 0.80

P(Z < z) - (1 - P(Z < z)) = 0.80

2P(Z < z) = 1.80

P(Z < z) = 0.90

So, the value of z is 1.282.

Now, put the values of height as follows:

-1.28=\dfrac{x_1-70}{4}

x_1 = 70- 5.128

x_1 = 64.872

1.28=\dfrac{x_2-70}{4}

x_2 = 1.28\times 4+70

x_2 = 75.128

x_2 \approx 75.13

Therefore, the height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches.

For more information, refer to the information given below:

brainly.com/question/23044118


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