The package of a replacement bulbs claims that these bulbs have an average life of 8000 hours. Assume that the lives of all such bulbs have a normal distribution with a meal of 8000 hours and a standard deviation of 400 hours. Let x be the average life of 17 randomly selected such bulbs.

a) find the mean and standard deviation of x

b) comment on the shape of its sampling distribution. Draw the population distribution and the sampling distribution on the same picture (include the picture in your pdf file)

c) find the probability that the mean life of a random sample of 17 such bulbs is less than the population mean by 150 or more.