Suppose the test scores of 600 students are normally distrib

Suppose the test scores of 600 students are normally distributed with a mean of 76 and standard deviation of 8. Find the number of students we would expect to score between 70 and 82.

Solution

here mean = 76 and standard deviation is 8

For x = 70 , z = (70 - 76) / 8 = -0.75 and for x = 82, z = (82 - 76) / 8 = 0.75

Hence P(70 < x < 82) = P(-0.75 < z < 0.75) = [area to the left of z = 0.75] - [area to the left of -0.75]

= 0.7734 - 0.2266 = 0.5468

this will be the probability =0.5468

the number will be 0.5468*600 = 328

and the percentage will be 54.68%