# Worksheet: Normal Distribution

In this worksheet, we will practice performing calculations on data that is normally distributed and using these calculations to make predictions and solve real-life applications.

**Q5: **

For a normally distributed data set with mean 32.1 and standard deviation 2.8, between which two values would you expect β 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

**Q6: **

The masses of a population of blackbirds are normally distributed with mean 103 g and standard deviation 11 g.

To the nearest integer, what percentage of blackbirds have masses less than 110 g?

To the nearest tenth, what percentage of blackbirds have masses greater than 124 g?

To the nearest integer, what percentage of blackbirds have masses between 95 g and 120 g?

**Q9: **

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

**Q10: **

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

**Q14: **

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

**Q19: **

The lengths of cylinders produced at a factory follow a normal distribution with mean 72 cm and standard deviation 5 cm. A cylinder is acceptable for sale if its length is between 64.4 cm and 73.4 cm. If a random sample of 1,000 cylinders is chosen, how many cylinders would be acceptable for sale?

**Q24: **

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.