Question

statistics

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 69.1 inches and a standard deviation of 3.0 inches. A study participant is randomly selected.b) Find the probability that a study participant has a height that is between 65 and 72 inches.

Answer 1

We are given

mean = 69.1

standard deviation = 3.0

We have to find the probability that the height will lie in between 65 and 72

Let the height be X

So, we have to find

So, let us first standardize the value on a normal standard scale:

Since we know that in the normal probability curve it follows the area of symmetricity that is the normal curve is a symmetric curve.

we can also write it as

So, since the curve is symmetric thus for the area between 0 to -1.36 must be equal to area between 0 to +1.36

So, we can write it as:

Now, we need to look up at the standard normal table,

we get:

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