Determine the mean of a set of a normally distributed data with a standard deviation

Question

Determine the mean of a set of a normally distributed data with a standard deviation of 4 and a 𝒛-score of 1.5 when 𝑥 = 73.

Answer 1

Use the formula for a z-score: z = (x - µ)/σ

(note: µ is the mean and σ is the standard deviation)

We know:

z = 1.5

x = 73

σ = 4

z = (x - µ)/σ

1.5 = (73 - µ)/4

6 = 73 - µ

µ + 6 = 73

µ = 67

The mean is 67.