Question

The average age of CEOs is 50 years. Assume the random variable is normally digtributad: If the standard deviation is 3 yeers, find the probutikty that the sge of a randomir selected CEO will be in the given range.

Between 47 and 53 years old

Answer 1

Using the Z-score method for a normal distribution with a mean of 50 and a standard deviation of 3, the probability that a CEO's age is between 47 and 53 is 68.26%.

Step-by-step explanation:

To calculate the probability that a randomly selected CEO is between 47 and 53 years old, given a normal distribution with a mean of 50 years and a standard deviation of 3 years, we will use the standard normal distribution and Z-scores. A Z-score represents how many standard deviations an element is from the mean.

First, let's find the Z-scores for the ages 47 and 53:

• Z for age 47 = (47 - 50) / 3 = -1
• Z for age 53 = (53 - 50) / 3 = 1

Next, we use the standard normal distribution table to find the area under the curve between these Z-scores. The table gives us the probability for values less than Z; therefore, we look up the values for Z = 1 and Z = -1.

The probability of Z < 1 is 0.8413 and the probability of Z < -1 is 0.1587. The probability of a CEO's age being between 47 and 53 is the difference between these probabilities:

Probability (47 < age < 53) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826

So, there is a 68.26% chance that a randomly selected CEO is between the ages of 47 and 53.