# Lesson Worksheet: Normal Distribution Mathematics

In this worksheet, we will practice using the normal distribution to calculate probabilities and find unknown variables and parameters.

Q1:

For the normal distribution shown, approximately what percentage of data points lie in the shaded region? Q2:

For the normal distribution shown, approximately what percent of data points lie in the shaded region? Q3:

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?

• A29.3 and 34.9
• B17.5 and 28.7
• C14.7 and 31.5
• D26.5 and 37.7
• E23.7 and 40.5

Q4:

For the normal distribution shown, approximately what percent of data points lie in the shaded region? Q5:

For a normally distributed data set, approximately what percentage of data points will lie within one standard deviation of the mean?

Q6:

For a normally distributed data set, approximately what percent of data points will lie within two standard deviations of the mean?

Q7:

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?

• A26.5 and 37.7
• B23.7 and 40.5
• C20.3 and 25.9
• D14.7 and 31.5
• E29.3 and 34.9

Q8:

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?

• A17.5 and 28.7
• B29.3 and 34.9
• C26.5 and 37.7
• D23.7 and 40.5
• E14.7 and 31.5

Q9:

Use tables to find the normal probability corresponding to a -score of 2.13.

Q10:

Use tables to find the normal probability corresponding to a -score of .

Q11:

Let be a normal random variable. Find .

Q12:

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

Q13:

Given a normal random variable such that , find the value of .

Q14:

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

Q15:

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

Q16:

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

Q17:

Let be a random variable which is normally distributed with mean and standard deviation . Given that and , calculate the values of and .

• A,
• B,
• C,
• D,

Q18:

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

Q19:

Let be a random variable which is normally distributed with mean 60 and standard deviation 5. Determine .

Q20:

Let be a normal random variable. Find .

Q21:

Let be a normal random variable. Find .

Q22:

Let be a random variable which is normally distributed with mean 73 and standard deviation 15. Determine .

Q23:

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

Q24:

Let be a random variable which is normally distributed with standard deviation 10. Given that , find the mean of .

Q25:

Let be a normal random variable such that and . Calculate .