Question

A set test papers is normally distributed with a standard deviation of 5. Riley scored an 83 with a z-score of -0.4, what was the mean?

Answer 1

We can use the formula for z-score to find the mean:

z = (x - μ) / σ

where z is the z-score, x is the observed value, μ is the population mean, and σ is the population standard deviation.

We know that Riley's z-score is -0.4:

-0.4 = (83 - μ) / 5

Multiplying both sides by 5, we get:

-2 = 83 - μ

Subtracting 83 from both sides, we get:

μ = 83 + 2 = 85

Therefore, the mean of the set test papers is 85.