The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken.
a. What are the expected value, standard deviation, and shape of the sampling distribution of ?
b. What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours?
c.What is the probability that the average life in the sample will be greater than 3,219.24 hours?
d. What is the probability that the average life in the sample will be less than 3,180.96 hours?
e. What is the probability that a light bulb lasts at least 4800 hours?
f. The probability of a bulb lasting less than 2300 is .1573. The maximum probability of a bulb lasting less than 2300 hours should be only 5%. What must change specifically? How would that change be obtained practically?
g. What change would be needed for a 4 pack of bulbs, on average, lasting less than 2300 hours? Assume the goal of 5% max as in f.