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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Please see the attachment for solution. If you need any clarification please ask me. Thanks.
body preview (15 words)
Please xxx the xxxxxxxxxx for xxxxxxxxx xx you xxxx xxx xxxxxxxxxxxxx please xxx xxx Thanks.
file1.doc preview (832 words)
1. Sears xxxxx xxx xxxxxxxxxxxx according xx xxxxx xxxxx xxxxxxx xxx xxxxx xxxxxxxxx for xxxxxxxxxxxx xxxx sampled xxx salespeople with following xxxxxx
xxx xxxxxxxxx xxx xxxxxxxxxxx that a randomly selected Sear's salesperson xxx xxxxx xxxxxxx xxxxx xxxxxxx xxx is xx excellent xxxxxxxxx for xxxxxxxxxxxx
P(Above xxxxxxx and Excellent) = 22/500 = xxxxx
(b) xxxxxxxxx the probability xxxx x randomly selected xxxxxx salesperson will xxxx average sales xxxxxxx an xxx xxxx xxxxxxxxx for advancement?
P(Stability xxxxxxx xxx Good) = 60/500 = 0.12
(c) Calculate the probability xxxx x randomly selected xxxxxx xxxxxxxxxxx will have xxxxx xxxxxxx xxxxx xxxxxxx xxx xxxx xxxxxxxxx for advancement?
xxxxxxxx xxxxxxx xxx xxxxx = xxxxxx x xxxxx
(d) Calculate xxx xxxxxxxxxxx that a randomly xxxxxxxx xxxxxx salesperson xxxx
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file2.xls preview (69 words)
|Poisson distributionxxx||Binomial distributionxxx||xxxxxx xxxxxxxxxxxx|
|x||xxxxxxxx||xx||xxxxxx||x||x||P(Z < xx|
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