Question

If a set of grades on statistics examination are approximately normally distributed with a mean of 74 and a standard deviation of 7.9, what is the lowest B if the top 10% of the students are given A's and the next 25% are given B's?

Answer 1

The lowest B grade is `77`

Explanation:

Given: normally distributed data, `mu = 74, sigma = 7.9`; A = top 10%, B is up to 25% less,

The probability for A's `= 1 - .10 = .90; " or "90%`

The probability for a B:
Lower percent value: `.1 + .25 = .35; " "1-.35 = .65`

is between `65% " and " 90 %`

`z = (x - mu)/sigma`

From a z-table the `.65` percent is about half way between `z = 0.38 " and " z = 0.39`. So let `z = 0.385`

Solve for the `x` value to find the lowest B grade:

`0.385 = (x - 74)/7.9`

`x = 0.385 * 7.9 + 74 = 77`

The lowest B grade is `77`