The life span of LED light bulbs is normally distributed with a mean and a standard deviation equal to 600 and 100 hours, respectively. The life span of fluorescent light bulbs is normally distributed with a mean and a standard deviation equal to 500 and 80 hours, respectively. a) Suppose a sample of four fluorescent light bulbs is selected. Find the probability that the mean life span of the fluorescent light bulbs is less than 643 hours. b) What is the probability that the average life span of 9 randomly selected LED light bulbs is 1 hour more than the average life span of 16 randomly selected fluorescent light bulbs? c) The manager of the company which produces LED light bulbs has determined that the proportion of LED light bulbs that have a life span change is thirty five percent. If a sample of 200 LED light bulbs is selected at random, what is the probability that less than forty percent of the LED light bulbs are with a changed life span? d) This part has no link to part a) to c). A researcher wants to estimate the mean yearly family expenditure on groceries. He believes that the standard deviation of the yearly expenditure is $1000. Determine with 99.5% confidence the number of families that must be sampled to estimate the mean yearly family expenditure on groceries to within $125