Statistics · Practice

Normal Distribution — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

What is the mean of the standard normal distribution?

Problem 2

Approximately what percentage of values in a normal distribution fall within 1 standard deviation of the mean?

Problem 3

What percentage of values in a normal distribution lie within 2 standard deviations of the mean?

Problem 4

A test has mean $\mu = 60$ and standard deviation $\sigma = 5$ . Find the $z$ -score for a grade of $70$ .

Problem 5

In a normal distribution, what is the probability that a value is above the mean?

Problem 6

Find $P(Z < 2)$ for a standard normal variable $Z$ .

Problem 7

An IQ test has $\mu = 100$ , $\sigma = 15$ . What IQ score corresponds to $z = -1$ ?

Problem 8

Find $P(Z > 1)$ for a standard normal variable $Z$ .

Problem 9

Find $P(-1 < Z < 1)$ for a standard normal variable $Z$ .

Problem 10

Find the $z$ -score at the 95th percentile of the standard normal distribution.

Problem 11

What percentage of data in a normal distribution lies within 3 standard deviations of the mean?