Lesson Worksheet: Normal Distribution Mathematics

For the normal distribution shown, approximately what percent of data points lie in the shaded region?

For a normally distributed data set with mean 32.1 and standard deviation 2.8, between which two values would you expect ‎ of the data set to lie?

Let be a standard normal random variable. Calculate .

Let be a random variable which is normally distributed with mean 68 and standard deviation 3. Determine .

Given that is a standard normal random variable and , find .

Suppose is a standard normal random variable. Given , find the value of .

Let be a random variable which is normally distributed with mean 63 and variance 144. Determine .

Suppose is normally distributed with mean and variance 196. Given that , find the value of .

Let be a random variable which is normally distributed with mean and standard deviation . Given that , find .

Let be a normal random variable. Find .