The heights of South African men are Normally distributed with a mean of 69 inches and a standard deviation of 4 inches. What is the probabi

Question

The heights of South African men are Normally distributed with a mean of 69 inches and a standard deviation of 4 inches. What is the probability that a randomly selected South African man is taller than 72 inches

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4 months 2021-10-08T18:09:30+00:00 1 Answer 0 views 0

the probability that a randomly selected South African man is taller than 72 inches is 0.2266

Step-by-step explanation:

The heights of South African men are Normally distributed with a mean of 69 inches and a standard deviation of 4 inches

population mean(m) = 69 inches

population standard deviation(s) = 4 inches

Therefore, the number of standard deviation above mean (z score) = (x – m)/s

In this case, x = 72 inches

z score = (72 – 69)/4 = 3/4 = 0.75

Probability that a randomly selected South African man is taller than 72 inches  P(x>72) = 1 – P(x<72) = 1 – z(0.75) using the z table,

P(x>72) = 1 – 0.77337 = 0.2266

therefore, the probability that a randomly selected South African man is taller than 72 inches is 0.2266