What is the data element with a z-score of 1.5, in a data set that has a mean of 50, and a standard deviation of 5?

Question

What is the data element with a z-score of 1.5, in a data set that has a mean of 50, and a standard deviation of 5?

Answer 1

The formula for the z-score is (Value - Mean)/Std. Deviation, or z = (x - µ)/σ.

z = 1.5; μ = 50; σ = 5

So 1.5 = (x - 50)/5

Can you solve for x to find the data element in the set with those characteristics?

Hint: start by multiplying both sides by 5 to eliminate the fraction.

Answer 2

Let x be the data element.

z = (x - mean) / (standard deviation)

1.5 = (x - 50) / 5

7.5 = x - 50

x = 57.5