Thousands of fluorescent light bulbs have been made at a factory.It is desired to determine the mean of all the light bulbs.A random sample of 70 fluorescent light bulbs has a mean life of 610 hours.Assume the population standard deviation is 36 hours.

a) Construct a 95% confidence interval for the population mean.

b) To construct the interval in part a, did you use the t-distribution or the standard normal distribution?Explain.

c) Which of the following are we 95% confident is in the confidence interval?

i) The usual amount of time a bulb lasts.

ii) The true population average of all thousands of bulbs of this type.

iii) The sample mean of the 70 bulbs.

d) Explain why a bulb that lasted 620 hours is NOT unusual, even though it is NOT in the confidence interval?