An electrical firm manufactures 100-watt light bulbs. These bulbs, according to specifications written on the package, have a mean life of 900 hours with a standard deviation of 50 hours. Assume that the distribution is symmetric about the mean. Give an upper bound to the probability that the life of a bulb win a new production batch will exceed 990 hours. Suppose that the mean is unknown but the standard deviation is 50 hours. What can be said about the probability that the life of a new bulb will be within 150 hours of the unknown mean for that batch?
How many new bulbs should be made so as to ensure, with a probability of at least 0.75, that the average life would be within 25 hours of the unknown mean? Assume each bulb is produced independently.