The lifetimes of lightbulbs produced by a particular manufacturer have mean 1,200 hours. and standard deviation 400 hours. The population distribution is normal. Suppose that you purchase nine bulbs, which can be regarded as a random sample from the manufacturer's output.

(a) What is the mean of the sample mean lifetime?

(b) What is the variance of the sample mean?

(c) What is the standard error of the sample mean?

(d) What is the probability that, on average, these nine lightbulbs have lifetimes of less than 1,050 hours?