Question

a normal distribution has a mean of 10 and a standard deviation of 1 what is the probability of selecting a number between 8 and 11

Answer 1

0.815

Explanation:

First, find the z-scores.

z = (x − μ) / σ

z₁ = (8 − 10) / 1

z₁ = -2

z₂ = (11 − 10) / 1

z₂ = 1

P(-2 < Z < 1) = P(Z < 1) − P(Z < -2)

Use a chart, calculator, or the empirical rule to find the probability.

Using the empirical rule:

P(-2 < Z < 1) = 0.84 − 0.025

P(-2 < Z < 1) = 0.815

Using a chart:

P(-2 < Z < 1) = 0.8413 − 0.0228

P(-2 < Z < 1) = 0.8185