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wrote...
Posts: 217
2 weeks ago
A biology professor responds to some student questions by e-mail. The probability model below describes the number of e-mails that the professor may receive from students during a day.



a. How many e-mails should the professor expect to receive each day?

b. What is the standard deviation?

c. If it takes the professor an average of ten minutes to respond to each e-mail, how much time should the professor expect to spend responding to student e-mails each day?
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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wrote...
Posts: 266
2 weeks ago
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a.  Let X = number of e-mails received.
   E(X) = 0(0.05) + 1(0.10) + 2(0.20) + 3(0.25) + 4(0.30) + 5(0.10) = 2.95 e-mails per day
b.  Var(X) = (0 - 2.95)2 (0.05) + (1 - 2.95)2 (0.10) + (2 - 2.95)2 (0.20)
           + (3 - 2.95)2 (0.25) + (4 - 2.95)2 (0.30) + (5 - 2.95)2(0.10)
         = 1.7475
    SD(X)  = = 1.32 e-mails per day
c. 10E(X) = 10(2.95) = 29.5 minutes per day
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