Question

Sergio is working on a research project involving the ages of students at Brooklyn College. After interviewing 500 students, he has determined that the average age of a Brooklyn College student is 20 years and 6 months. He has further determined that the range of ages of the students on campus follows a normal distribution with a standard deviation of 2 years. What is the probability of a randomly chosen student being exactly 21 years old

Answer 1

The probability of of a randomly chosen student being exactly 21 years old.

= 1.293

Explanation:

Step(i):-

Given Population size n = 500

Mean of the Population = 20 years and 6 months

=
`20 + (6)/(12) = 20 +0.5 = 20.5 years`

Standard deviation of the Population = 2 years

Let 'X' be the range of ages of the students on campus follows a normal distribution

Let x =21

`Z = (x-mean)/(S.D)`

`Z = (x-mean)/(S.D) = (21-20.6)/(2) =0.2`

The probability of a randomly chosen student being exactly 21 years old.

P( Z≤21) = 0.5 + A( 0.2)

= 0.5 +0.793

= 1.293