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Submitted by Jdpt3 on Tue, 2012-06-12 20:09
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 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?

Submitted by StatSolver on Tue, 2012-06-12 21:13
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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.

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xx Sears xxxxx its xxxxxxxxxxxx xxxxxxxxx to xxxxx sales ability and xxxxx potential for advancement. xxxx xxxxxxx xxx salespeople xxxx following data:

xxxxxxxxxxxx
 xxxx 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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# Sheet1

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 xxxxxxx 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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# Q1

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 xx 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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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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