Homework SourseA new Bookstore website receives 13 hits each day The probab
A new Bookstore web-site receives 13 “hits” each day. The probability that a “hit” results in a purchase is 0.3300.
-Thirteen people enter the site … what is the probability that more than nine make a purchase?
-Thirteen people enter the site … what is the probability that any number except eight make a purchase?
-Thirteen people enter the site…what is the probability that more than four but fewer than eight make a purchase? (Hint: This could also be stated as 5, 6, or 7 make a purchase.)
Solution
a)
Note that P(more than x) = 1 - P(at most x).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 13
p = the probability of a success = 0.33
x = our critical value of successes = 9
Then the cumulative probability of P(at most x) from a table/technology is
P(at most 9 ) = 0.998490516
Thus, the probability of at least 10 successes is
P(more than 9 ) = 0.001509484 [answer]
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b)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 13
p = the probability of a success = 0.33
x = the number of successes = 8
Thus, the probability is
P ( 8 ) = 0.024437911
Thus,
P(not 8) = 1 - P(8) = 0.975562089 [answer]
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c)
Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)
Here,
x1 = 5
x2 = 7
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 13
p = the probability of a success = 0.33
Then
P(at most 4 ) = 0.562370328
P(at most 7 ) = 0.967365615
Thus,
P(between x1 and x2) = 0.404995286 [answer]
