Question

[3] A new school initiative was to investigate what could be done to enhance the middle 40% of students at a school considered at risk. If the average score of the MCA exam was 77 with standard deviation of 8.3, what is the minimum and maximum score to be considered in the middle 40%

Answer 1

Here we have = 77, = 8.3

Also we have middle 40% .

Remaining area is 1 - 0.40 = 0.60 . Hence due to symmetry, area to the left = area to the right = 0.30

Here we have,

p ( Z < z_a ) = 0.30

So z_a = -0.52 ----------( using excel formula " =norm.s.inv(0.30)" )

a = -0.52 * 8.3 + 77 = 72.68

Also , Let we have area,

p ( Z < z_b ) = 0.70

So, z_b = 0.52 --------( Using excel formula " =norm.s.inv(0.70)" )

b = 0.52 * 8.3 + 77 = 81.32

So minimum score is 72.68 and maximum score is 81.32.