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