The average lifetime of a light bulb is 3000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken.
(a) What is the expected value, standard deviation, and shape of the sampling distribution of ?
(b) What is the probability that the average lifetime in the sample will be between 3670.56 and 3809.76 hours?
(c) What is the probability that the average life time in the sample will be equal to or greater than 3219.24 hours?
(d) What is the probability that the average lifetime in the sample will be equal to or less than 3180.96 hours?
(e) How large of a sample needs to be taken to provide a 0.01 probability that the average life time in the sample will be equal to or greater than 3219.24 hours