Question

Help!

In a certain distribution, the mean is 100 with a standard deviation of 5. At least what fraction of the numbers are between the following pair of numbers ? 80 and 120.

Answer 1

Explanation:

To solve for this we would be using z score formula

z = (x - μ) / σ

x = raw score

μ = mean

σ = Standard deviation

We are told in the question to find the fraction of numbers between 80 and 120

let x1 = 80 and x2= 120 with the mean μ = 100 and standard deviation σ = 5.

z1 = (x1 - μ) / σ = (80-100) / 5 = -20/5 = -4

z2 = (x2 - μ) / σ = (120 - 100) / 5 = 20/5 = = 4

From tables, P(z <= -4) = 0.00003

P(z <= 4) = 0.99997

Then, the probability would give us, P(-4 ≤ z ≤ 4) = 0.99997 - 0.99997 =