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

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

To write a mixed number as an improper fraction, first multiply the denominator by the whole number and add the numerator.

5 × 8 = 40

40 + 2 = 42

Lastly, put the new numerator over the original denominator which in this case was 5.

42/5