Answer:
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:
[tex]z=\frac{x-\mu}{\sigma}=\frac{50-56}{4}=\frac{-6}{4}= -1.5[/tex]
For x=55:
[tex]z=\frac{x-\mu}{\sigma}=\frac{55-56}{4}=\frac{-1}{4}=-0.25[/tex]
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:
[tex]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[/tex]
There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that:
Mean = 56, standard deviation = 4, For 50:
z = (50 - 56) / 4 = -1.5
For 44:
z = (55 - 56) / 4 = -0.25
P(50 < x < 55) = P(z < -0.25) - P(z < -1.5) = 0.4013 - 0.0668 = 33.45
There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.
Find out more on z score at: https://brainly.com/question/25638875
