__Instructions:__Answer the following four questions. Write legibly and show all work. Begin each numbered question on a fresh page. Unsupported answers will receive zero points. You must work independently.

__Due:__ Tuesday 6/12, 11:59pm

1. Sears rates its salespersons according to their sales ability and their potential for advancement. They sampled 500 salespeople with following data:

(a) Calculate the probability that a randomly selected Sear’s salesperson has above average sales ability and is an excellent potential for advancement?

(b) Calculate the probability that a randomly selected Sear’s salesperson will have average sales ability an and good potential for advancement?

(c) Calculate the probability that a randomly selected Sear’s salesperson will have below average sales ability and fair potential for advancement?

(d) Calculate the probability that a randomly selected Sear’s salesperson will have an excellent potential for advancement given they also have above average sales ability?

(e) Calculate the probability that a randomly selected Sear’s salesperson will have an excellent potential for advancement given they also have average sales ability?

2.A study by the Information Technology department at WPU revealed company employees receive an average of four e-mails per hour. Assume the arrival of these e-mails is approximated by the Poisson distribution.

(a) What is the probability , Prof. Smith, received exactly one e-mail between 4pm and 5pm yesterday?

(b) What is the probability he did not receive any e-mail during this period**? **

(c) What is the probability he received ten or more e-mails during the same period?

3. A recent study in NJ showed that 50% of all patients will return to the same dentist. Suppose nine patients are selected at random, what is the probability that:

(a) Exactly five of the patients will return?

(b) All nine will return?

(c) At least eight will return?

(d) At least one will return?

(e) How many patients would be expected to return to the same dentist, i.e., what is the mean of the distribution?

4. A recent study of long distance phone calls made from WPU, showed that the length of the calls follows the normal probability distribution with a mean of 3.2 minutes per call and a standard deviation of 0.50 minutes.

(a) What fraction of the calls last between 3.2 and 4 minutes?

(b) What fraction of the calls last more than 4 minutes?

(c) What fraction of the calls last between 4 and 4.5 minutes?

(d) What fraction of the calls last between 3 and 4.5 minutes?

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