Delta International delivers approximately one million packages a day between East Asia and the United States. A random sample of the daily number of package delivery failures over the past six months provided the following results: 15, 10, 8, 16, 12, 11, 9, 8, 12, 9, 10, 8, 7, 16, 14, 12, 10, 9, 8, 11. There was nothing unusual about the operations during these days and, thus, the results can be considered typical. Using these data and your understanding of the delivery process answer the following: 1. What probability model should be used and why? 2. What is the probability of 10 or more failed deliveries on a typical future day? 3. What is the probability of less than 6 failed deliveries?

Solution 1. Use the Poisson probability distribution because the random variable is the number of occurrences of a certain event (delivery failures) in a given continuous interval (one day). 2. First, use the given data to determine an estimate for the expected number of failures per day. = 15+10+...+11 20 = 10.75 x P( X = x)(P ayattentionhereIreportthecumulativedistributionfunction) 1.00 0.0003 2.00 0.0015 3.00 0.0059 4.00 0.0179 5.00 0.0435 6.00 0.0895 7.00 0.1601 8.00 0.2549 9.00 0.3682 10.00 0.4900 Now we compute the cumulative distribution function: P(X 10) = 1 P(X 9) = 1 0.3682 = 0.6318 3. P(X < 6) = P(X 5) = 0.0435

CAN YOU EXPLAIN ME THE SOLUTION PLEASE, I DONT GET IT