Mathematics: Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. if 64 men are randomly selected, find the probability that they have a mean height between 68 and 70 inches.

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Assume that the heights of men are normally distributed

alexnunez07

14.03.2022

0.9958

Step-by-step explanation:

We assume that the heights of men are normally distributed with

Mean : $\mu=69.0\text{ inches}$

Standard deviation : $\sigma=2.8\text{ inches}$

Sample size : n=64

The value of z-score is given by:

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Let x be the height of the randomly selected men.

For x= 68

$z=\dfrac{68-69}{\dfrac{2.8}{\sqrt{64}}}\approx-2.86$

For x= 70

$z=\dfrac{70-69}{\dfrac{2.8}{\sqrt{64}}}\approx2.86$

Now, the probability that they have a mean height between 68 and 70 inches is given by :-

P(68

Hence, the probability that they have a mean height between 68 and 70 inches = 0.9958

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