How Many Test Runs for a Sample Size?

The manufacturer of batteries used in small electric appliances wants to
establish the average life of a battery. A random sampleof 12 batteries yields a sample meanof 34.2 hours, and a sample standard deviationof 5.9 hours. Give a 95% confidence intervalfor the average life of a battery. Assume the underlying distribution is normal.

How many test runs (i.e. minimum sample size) of an automobile are required for determining it’s average miles-per-gallon rating on the highway to within 2 miles per gallon with 95% confidence, if a good guess is that the varianceof the population of miles per gallon is about 100?

Please see the attached file.

I have 5 questions that are supposed to help me review my reading material. Here is one. I would like to work with one OT for all of them if possible so that I can have conversation about my understanding. Here is the first question.
Thank You-Gail
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The manufacturer of batteries used in small …

The solution attaches a Word document showing how many test runs are needed to make a confident assessment of batteries.