The average age of CEOs is 56 years. Assume the variable is normally distributed. If the SD is four years, find the probability that the age of randomly selected CEO will be between 50 and 55 years old.

Answer: the probability that the age of randomly selected CEO will be between 50 and 55 years old is 0.334

Step-by-step explanation:

Assuming that the age of randomly selected CEOs is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = age of randomly selected CEOs.

µ = mean age

σ = standard deviation

From the information given,

µ = 56 years

σ = 4 years

We want to find the probability that the age of randomly selected CEO will be between 50 and 55 years old. It is expressed as

P (50 ≤ x ≤ 55)

For x = 50,

z = (50 - 56) / 4 = - 1.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.067

For x = 55,

z = (55 - 56) / 4 = - 0.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.401

Therefore,

P (50 ≤ x ≤ 55) = 0.401 - 0.067 = 0.334