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

Answer:

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

= 1.293

Step-by-step explanation:

Step(i):-

Given Population  size n = 500

Mean of the Population = 20 years and 6 months

                                       = $20 + \frac{6}{12} = 20 +0.5 = 20.5 years$

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

            $Z = \frac{x-mean}{S.D}$

            $Z = \frac{x-mean}{S.D} = \frac{21-20.6}{2} =0.2$

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