Question

A sample of scores is normally distributed with a mean equal to 27 and a variance equal to 16. What proportion is under 20

Answer 1

Solution:
Given in the question
Sample of scores is normally distributed with
Mean() = 27
Variance(^2) = 16
Standard deviation() = sqrt(16) = 4
We need to calculate probability or proportion under 20 which can be calculated as
Here we will use standard normal distribution, First we will calculate Z-score which can be calculated as
Z-score = (X-)/) = (20-27)/4 = -1.75
From Z table we found p-value
P(X<20) = 0.0401
So there is 4.01% proportion is under 20.