Business Statisticks
Business Statistics
Second Exam
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.
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Please xxx the attachment for solution. If you need any clarification xxxxxx xxx xxx Thanks.
file1.doc preview (737 words)
xx Sears xxxxx its xxxxxxxxxxxx xxxxxxxxx to xxxxx sales ability and xxxxx potential for advancement. xxxx xxxxxxx xxx salespeople xxxx following data:
xxxxxxxxxxxxxxxx | Good | xxxxxxxxx | xxxxx | ||
Above xxxxxxx | 16 | 12 | xx | 50 | |
xxxxxxxxx average | 45 | 60 | xx | xxx | |
below average | 93 | 72 | 135 | 300 | |
xxxxx | 154 | xxx | 202 | 500 |
xxx Calculate xxx probability xxxx a xxxxxxxx selected xxxxxx xxxxxxxxxxx has above xxxxxxx sales xxxxxxx and xx an excellent xxxxxxxxx for advancement?
P(Above average and Excellent) = xxxxxx x 0.044
(b) xxxxxxxxx xxx probability xxxx x xxxxxxxx xxxxxxxx Sear's xxxxxxxxxxx xxxx have xxxxxxx sales xxxxxxx xx and xxxx xxxxxxxxx xxx xxxxxxxxxxxx
P(Stability xxxxxxx xxx xxxxx x 60/500 = xxxx
(c) xxxxxxxxx the xxxxxxxxxxx that a randomly selected Sear's salesperson will xxxx xxxxx xxxxxxx sales xxxxxxx and xxxx potential for xxxxxxxxxxxx
xxxxxxxx xxxxxxx and Fair) x 93/500 = xxxxx
(d) xxxxxxxxx xxx xxxxxxxxxxx that a randomly xxxxxxxx xxxxxx xxxxxxxxxxx xxxx xxxx xx excellent potential for advancement given they also xxxx xxxxx xxxxxxx sales ability?
P(Excellent|Above xxxxxxxx x 22/50 x 0.44
xxx xxxxxxxxx the xxxxxxxxxxx xxxx a randomly xxxxxxxx Sear's xxxxxxxxxxx will have an excellent xxxxxxxxx xxx xxxxxxxxxxx xxxxx they xxxx have xxxxxxx xxxxx xxxxxxxx
xxxxxxxxxxxxx Stability average) x 45/150 = 0.30
2.A study by xxx Information xxxxxxxxxx xxxxxxxxxx xx xxx revealed xxxxxxx xxxxxxxxx xxxxxxx an xxxxxxx of xxxx e-mails per xxxxx xxxxxx xxx
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file2.xls preview (33 words)
Sheet1
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx | Binomial distribution | Normal distribution | ||||
x | xxxxxx | x | xxxxxx | x | z | xxx < xx |
0 | xxxxxx | x | 0.0020 | xxxx | 0 | xxxxxxxxxxxx |
x | 0.0733 | x | xxxxxx | x | 1.6 | xxxxxx |
2 | xxxxxx | x | 0.0703 | xxx | xxx | 0.9953 |
x | xxxxxx | x | xxxxxx | 3 | -0.4 | xxxxxx |
x | xxxxxx | x | 0.2461 | |||
x | xxxxxx | 5 | xxxxxx | |||
x | 0.1042 | 6 | xxxxxx | |||
7 | 0.0595 | x | xxxxxx | |||
x | xxxxxx | 8 | xxxxxx | |||
x | 0.0132 | 9 | 0.0020 | |||
Fair | xxxx | xxxxxxxxx | xxxxx | |||
Above average | xx | 12 | xx | 50 | ||
stability average | xx | 60 | xx | xxx | ||
below xxxxxxx | 93 | xx | 135 | xxx | ||
Total | xxx | 144 | 202 | 500 |
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Answer file with formula and step by step calculation with printable format is attached. Feel free to contact for any further assistance.
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file1.xlsx preview (698 words)
Q1
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | Data: | Potential xxx advancement | |||
Sales xxxxxxx | Fair | xxxx | xxxxxxxxx | xxxxx | |
x | G | H | I | ||
xxxxx xxxxxxx | x | 16 | 12 | 22 | 50 |
xxxxxxx | x | xx | xx | 45 | xxx |
xxxxx average | 7 | 93 | xx | xxx | xxx |
xxxxx | x | xxx | xxx | 202 | xxx |
xxxxxxxxx | |||||
xxx | Calculate the xxxxxxxxxxx that x randomly xxxxxxxx xxxx’s xxxxxxxxxxx xxx xxxxx xxxxxxx xxxxx ability and xx xx xxxxxxxxx potential for xxxxxxxxxxxx | ||||
xxxxxx | x | 0.27 | |||
(b) | Calculate xxx probability that a xxxxxxxx selected xxxx’x xxxxxxxxxxx will have average xxxxx ability xx xxx good potential for xxxxxxxxxxxx | ||||
=G6/I8 | = | xxxx | |||
(c) | xxxxxxxxx xxx xxxxxxxxxxx that a randomly xxxxxxxx Sear’s salesperson xxxx have xxxxx average sales ability xxx fair xxxxxxxxx xxx advancement? | ||||
=F5/I8 | x | xxxx | |||
xxx | Calculate the probability that x randomly selected Sear’x salesperson xxxx xxxx xx excellent xxxxxxxxx for advancement xxxxx they xxxx have xxxxx average xxxxx xxxxxxxx | ||||
=H7/H8 | x | xxxx | |||
(e) | xxxxxxxxx xxx xxxxxxxxxxx that x randomly xxxxxxxx Sear’s salesperson xxxx have xx |
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the answer is in attached file
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xxxxx xxxxx its xxxxxxxxxxxx according xx their sales ability xxx their xxxxxxxxx xxx advancement. xxxx sampled 500 salespeople with xxxxxxxxx xxxxx
(a) xxxxxxxxx the xxxxxxxxxxx xxxx a randomly xxxxxxxx Sear's xxxxxxxxxxx xxx above average sales ability xxx is xx excellent potential xxx advancement? xxxxxxxx xxxxx
(b) Calculate the probability that x xxxxxxxx xxxxxxxx Sear's xxxxxxxxxxx xxxx have xxxxxxx xxxxx xxxxxxx and xxxx potential for xxxxxxxxxxxx xxxxxxxxxxxx
xxx xxxxxxxxx the xxxxxxxxxxx that x randomly selected xxxxxx salesperson xxxx xxxx below xxxxxxx sales ability xxx fair xxxxxxxxx for xxxxxxxxxxxx xxxxxxxxxxxxx
(d) xxxxxxxxx xxx xxxxxxxxxxx that a randomly selected Sear's salesperson xxxx have xx excellent potential for xxxxxxxxxxx xxxxx xxxx also have xxxxx average xxxxx ability? xxxxxxxxxxxxxxxxxxxxx
xxx xxxxxxxxx xxx probability xxxx a xxxxxxxx xxxxxxxx Sear's salesperson will have xx excellent potential xxx xxxxxxxxxxx xxxxx xxxx xxxx have average sales xxxxxxxx x
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