On a test that has a normal distribution, a score of 19 falls one standard deviation below the mean, and a score of 40 falls two standard deviations above the mean. Determine the mean of this test.

Hi there!

We can use the following equation:

z = amount of standard deviations away a value is from the mean (z-score)

σ = standard deviation

x = value

μ = mean

Plug in the knowns for both and rearrange to solve for the mean:

Other given:

Set both equal to each other and solve:

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: