# Lesson Worksheet: Finding Means and Standard Deviations in Normal Distributions Mathematics

In this worksheet, we will practice finding an unknown mean and/or standard deviation in a normal distribution.

**Q1: **

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

**Q2: **

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

**Q3: **

Suppose that is a normal random variable whose mean is and standard deviation is . If Β and , find using the standard normal distribution table.

**Q4: **

Let be a random variable which is normally distributed with mean 65. Given that , find the variance.

**Q5: **

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,

**Q6: **

Consider the random variable . Given that and , find the value of and the value of . Give your answers to one decimal place.

- A,
- B,
- C,
- D,
- E,

**Q7: **

The heights of a sample of flowers are normally distributed with mean and standard deviation 12 cm. Given that of the flowers are shorter than 47 cm, determine .

**Q8: **

The heights of a group of students follow a normal distribution with a standard deviation of 20 cm. The probability that a studentβs height is less than or equal to 180 cm is equal to the probability that a standard normal variable is less than or equal to 2.2. Find the mean height of the group of students.

**Q9: **

The lengths of a certain type of plant are normally distributed with a mean and standard deviation . Given that the lengths of of the plants are less than 75 cm, find the variance.

**Q10: **

The monthly salaries of workers at a factory are normally distributed with mean and standard deviation 200 pounds. Given that of the workers earn more than 1,851 LE, find .