Question

If the heights of women are normally distributed with a mean of 65.0 inches and a standard deviation of 2.5 inches and the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. A male patient's height in this experiment is 71 inches. Answer the series questions below. (Formulas and explanations needed)

(a) Determine the probability of finding a person of same gender as the patient to be exactly at patient's height.

(b) Determine what percentage of people of same gender would be taller than the patient. In case the patient's height is "exactly" 65 inches or 69 inches, add 1 inch to it and keep working with that new height.

(c) If someone of patient's gender were randomly selected, what would be the probability that the selected person would be shorter than the patient?

(d) What is the minimum height of a person of the patient's gender to be within 2 inches of patient's height (between "patient's height -2 inches" and "patient's height + 2 inches")?

(e) What is the minimum height of a person of patient's gender to be the "Top 16% Tall patients"?

(f) If 49 people of patient's gender are randomly selected, determine the probability that their mean height would exceed the patient's height.

Answer 1

Let M be the random variable denoting the height of Males

Let W be the random variable denoting the height of Women,

Given,

Part a
To find P(M=71) =

Thus the probability that a male with height 71 inches is found, is 0.1104

Part b

To find the percentage of males with height greater than 71 inches , ie. to compute,

Answer + 23.76%

Part c

To find the probability that a male's height is less than 71 i.e. to find ,

Answer : Required probability is 0.7624

Part d

The minimum height of a male person,to be in the height interval [71-2,71+2] = [69,73] is minimum of the slot = 69 inches

Please comment out any queries regarding my solution.

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