# Lesson Worksheet: Normal Distribution Mathematics

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

**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

**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 .