1. A machine manufactures bolts to a set length with a standard deviation of 2.5 mm.

A random sample of 20 bolts is checked and found to have a mean length of 75.2 mm.

Find the 99% confidence interval for the mean length of the bolts.

2. A random sample of 100 is taken from a population.

The sample is found to have a mean of 23 and a standard deviation of 7.

Find a 90% confidence interval for the mean of the population.

3. 60 people were asked to measure their pulse rates after completing a 3 km run.

The mean was 105 beats and the standard deviation was 8 beats.

Construct a 95% confidence interval for the mean of the population of people.

4.

A type of golf ball is tested by dropping it onto a hard surface from a height of 1 metre.

The height it bounces is known to be normally distributed with a standard deviation of 3.6 cm.

If a sample of 100 balls are tested and the mean height of the bounces is 82 cm.

Find a. 90% b. 95% and c. 99% confidence intervals for the mean of the bounce of the golf ball.

5.

A sample of stalactites (a type of rock formation) found in a glow worm cave produced the following lengths in cm:

9.6
16.9
15.1
14.3
15.9
17.2
13.0
17.1
15.4
16.2
4.5
20.3
21.2
15.7

Assuming that this sample came from a normal population with a variance of 4.4, calculate a 95% confidence interval for the mean length of stalactites in the cave.

6.

A doctor conducts a small survey with a random sample of his patients, measuring their cholesterol levels.

Here is his data (the measurements are in m.mol/L):

3.6
6.9
5.1
4.2
5.5
7.2
3.0
5.8
4.9
9.9
7.1
5.4
6.2
4.5
6.3
8.2
5.7
4.4
7.9
3.2

Find an 80% confidence interval for the mean cholesterol level of his patients.