5.27 Sara is a salesperson for Camera\'s Etc. which is a retailer for high-end d
ID: 3133286 • Letter: 5
Question
5.27
Sara is a salesperson for Camera's Etc. which is a retailer for high-end digital cameras? Historically, Sara has averaged selling 2.1 extended warranties per day for cameras that she sells. Assume the number of camera warranties that Sara sells per day follows the Poisson distribution.
a. What is the probability that Sara will sell five extended warranties tomorrow?
b. What is the probability that Sara will not sell an extended warranty tomorrow?
c. What is the probability that Sara will sell more than two extended warrantes tomorrow?
d. What is the standard deviation for this distribution?
Explanation / Answer
a)
Note that the probability of x successes is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 2.1
x = the number of successes = 5
Thus, the probability is
P ( 5 ) = 0.041677035 [ANSWER]
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b)
Note that the probability of x successes is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 2.1
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.122456428 [ANSWER]
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c)
Note that P(more than x) = 1 - P(at most x).
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 2.1
x = our critical value of successes = 2
Then the cumulative probability of P(at most x) from a table/technology is
P(at most 2 ) = 0.649631352
Thus, the probability of at least 3 successes is
P(more than 2 ) = 0.350368648 [ANSWER]
*********************
d)
As
standard deviation = sqrt(u) = sqrt(2.1) = 1.449137675 [ANSWER]
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