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.

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

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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

case(ii):-  when  x = 98

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

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