Question

The scores on a math test are normally distributed with a mean of 74 and a standard deviation of 8. The test scores range from 0 to 100. Seven students had test scores between 82 and 98. Estimate the number of students who took the test.

Answer 1

Answer:

The Estimate the number of students who took the scores between  82 and 98 = 16

Step-by-step explanation:

Explanation:-

Given data The scores on a math test are normally distributed with a mean μ = 74  

standard deviation of Population

                                               S.D (σ) = 8

Let 'x' be the random variable of Normal distribution

case(i):-  when  x = 82

            $Z = \frac{x-mean}{S.D}$

           $Z = \frac{82-74}{8} = 1$

     

case(ii):-  when  x = 98

            $Z = \frac{x-mean}{S.D}$

           $Z = \frac{98-74}{8} = 3$

The probability that test scores between 82 and 98.

P(82≤x≤98) = P(1≤z≤3)

                 = P(z≤3) - P(z≤1)

                 = 0.5+A(3)-(0.5+A(1))

                =  A(3) -A(1)

               = 0.4986 - 0.3413

               = 0.1573

Final answer:-

The Estimate the number of students who took the scores between  82 and 98

             = 100 X 0.1573 = 15.73 ≅16