Suppose the heights of women at a college are approximately Normally distributed with a mean of 65 inches and a population standard deviation of 1.5 inches. What height is at the 20 th percentile? Include an appropriately labeled sketch of the Normal curve to support your answer.

Height at the 20th percentile = 63.74

Step-by-step explanation:

We are given that the heights of women at a college are approximately Normally distributed with a mean of 65 inches and a population standard deviation of 1.5 inches.

Since, X ~ N()

The z score probability distribution is given by;

            Z = ~ N(0,1)

As we are given that we have to find the height at the 20th percentile, which means the value of x below which the z has a area of 20% ;

 P(X < x) = 0.20

 P( < ) = 0.20

 P(Z < ) = 0.20

Now, in z normal table, the critical value of x having area less than 20% is -0.8416, i.e;

              = -0.8416

              x = 65 - (0.8416 * 1.5)

              x = 65 - 1.2624 = 63.74 inches

Therefore, height at the 20th percentile is 63.74 inches .

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