A restaurant manager is interested in taking a more statisticalapproach to predicting customer load. She begins the process bygathering data. One of the restaurant hosts or hostesses isassigned to count customers every five minutes from 7 P.M. until 8P.M. every Saturday night for three weeks. The data are shown here.After the data are gathered, the manager computes lambda using thedata from all three weeks as one data set as a basis forprobability analysis.What value of lambda did she find? Assume thatthese customers randomly arrive and that the arrivals are Poissondistributed. Use the value of lambda computed by the manager andhelp the manager calculate the probabilities in parts (a) through(e) for any given five-minute interval between 7 P.M. and 8 P.M. onSaturday night. Number of Arrivals Week 1 Week 2 Week 3 3 1 5 6 2 34 4 5 6 0 3 2 2 5 3 6 4 1 5 7 5 4 3 1 2 4 0 5 8 3 3 1 3 4 3 a. Whatis the probability that no customers arrive during any givenfive-minute interval? b. What is the probability that five or morecustomers arrive during any given five-minute interval? c. What isthe probability that during a 10-minute interval fewer than fourcustomers arrive? d. What is the probability that between four andsix (inclusive) customers arrive in any 10-minute interval? e. Whatis the probability that exactly six customers arrive in any15-minute interval? *Round your answers to 4 decimal places whencalculating using Table A.3. **Round your answer to 4 decimalplaces, the tolerance is +/-0.0005. a. P(x = 0) = * b. P(x ? 5) = *c. P(x < 4 | 10 minutes) = * d. P(4 ? x ? 6 | 10 minutes) = * e.P(x = 6 | 15 minutes) = **
