Suppose that the time taken for food to spoil using a certain packaging method has an exponential distribution with a mean of 8 days. (If necessary, use the normal approximation to binomial, NOT the sampling distribution of the sample proportion.) [Note: When needed, correct answers use the provided z-table on eClass, but Excel can also be appropriately used.] (a) What is the probability that a single packet will contain spoiled food after 12 days? (Round your answers to 3 decimal places, if needed.) (Note: The exact unrounded value should be used for remaining questions.) (b) If a random sample of 100 packets are tested after 12 days, what are the expected value and the standard deviation of the number of packets that will be found with spoiled food? (Round your answers to 3 decimal places, if needed.) Expected value: Standard deviation: (c) What is the probability that at least 70 of the packets will contain spoiled food? (Round your answers to 4 decimal places, if needed.) Check