Question

 (6 pts) 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 1

The probability that the age of a randomly selected CEO will be between 50 and 55 years old is approximately 0.3345.

Step-by-step explanation:

To find the probability that the age of a randomly selected CEO will be between 50 and 55 years old, we need to calculate the z-scores for both values and then use the standard normal distribution table.

Step 1: Calculate the z-score for 50 years old:

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

Step 2: Calculate the z-score for 55 years old:

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

Step 3: Use the standard normal distribution table to find the area to the left of each z-score:

P(z < -1.5) = 0.0668

P(z < -0.25) = 0.4013

Step 4: Calculate the probability between the two z-scores:

P(-1.5 < z < -0.25) = P(z < -0.25) - P(z < -1.5) = 0.4013 - 0.0668 = 0.3345

Therefore, the probability that the age of a randomly selected CEO will be between 50 and 55 years old is approximately 0.3345.

Answer 2

The probability that the age of a randomly selected CEO will be between 50 and 55 years old is 0.334.

Step-by-step explanation:

We have a normal distribution with mean=56 years and s.d.=4 years.

We have to calculate the probability that a randomly selected CEO have an age between 50 and 55.

We have to calculate the z-value for 50 and 55.

For x=50:

`z=(x-\mu)/(\sigma)=(50-56)/(4)=(-6)/(4)= -1.5`

For x=55:

`z=(x-\mu)/(\sigma)=(55-56)/(4)=(-1)/(4)=-0.25`

The probability of being between 50 and 55 years is equal to the difference between the probability of being under 55 years and the probability of being under 50 years:

`P(50<x<55)=P(x<55)-P(x<50)\\\\P(50<x<55)=P(z<-0.25)-P(z<-1.5)\\\\P(50<x<55)=0.40129-0.06681\\\\P(50<x<55)=0.33448`