Question: The lifetimes of lightbulbs produced by a particular manufacturer have mean 1,200 hours and standard deviation 400 hours. Suppose that you purchase nine bulbs, which can be considered a random sample from the manufacturer’s output and the mean lifetime in your sample is 1,050 hours.

1. Is it necessary to assume that the lifetimes can be modelled by a normal distribution to use the Central Limit Theorem?
2. What is the expectation of the sample mean?
3. What is the standard error of the sample mean?
4. What is the probability of getting such a small sample mean if it is true what the company claims about the lifetime of its lightbulbs?

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