A normal distribution has a mean of µ = 70 with σ = 10. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 82?

0.11507

Step-by-step explanation:

A normal distribution has a mean of µ = 70 with σ = 10. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 82?

We solve this question using z score formula:

z = (x-μ)/σ,

where

x is the raw score = 82

μ is the population mean = 70

σ is the population standard deviation = 10

z = 82 - 70/10

z = 1.2

Probability value from Z-Table:

P(x<82) = 0.88493

P(x>82) = 1 - P(x<82) = 0.11507

Therefore, the probability that the score will be greater than X = 82 is

0.11507