Question

A normal distribution has a mean of µ = 100 with σ = 20. if one score is randomly selected from this distribution, what is the probability that the score will be less than x = 84?​

Answer 1

Given: Mean of Normal distribution μ = 100, standard deviation σ =20

We have to find the probability that the score will be less than X=84

P(X < 84)

The z-score for x=84 is

Z = $\frac{x-mean}{standard deviation}$

Z = $\frac{84-100}{20}$

Z = -0.8

We have to find probability that Z < -0.8

Using Z score table to find the probability below z=-0.8 we get

P(Z < -0.8) = 0.2119

Hence the probability that the score will be less than x = 84 is 0.2119