Question

2. An electrical firm manufactures light bulbs that have a length of life that is normally distributed with a standard deviation of 40 hours. A random sample of 30 bulbs has an average life of 780 hours.

a. Find a 96% confidence interval for the population mean of all bulbs produced by this firm.
b. How large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?

3. A random sample of 8 cigarettes of a certain brand has an average nicotine content of 3.5 milligrams and a standard deviation of 0.9 milligrams. Construct a 99% confidence interval for the true average nicotine content of this particular brand of cigarettes, assuming normal distribution.