Binominal Distributions Worksheet With Answer Key - Helm 2008 Section 372 Page 9
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Example 11
A University Engineering Department has introduced a new software package called
SOLVIT. To save money, the University’s Purchasing Department has negotiated
a bargain price for a 4-user licence that allows only four students to use SOLVIT
at any one time. It is estimated that this should allow 90% of students to use
the package when they need it. The Students’ Union has asked for more licences
to be bought since engineering students report having to queue excessively to use
SOLVIT. As a result the Computer Centre monitors the use of the software. Their
findings show that on average 20 students are logged on at peak times and 4 of
these want to use SOLVIT. Was the Purchasing Department’s estimate correct?
Solution
4
P(student wanted to use SOLVIT ) =
= 0.2
20
Let X be the number of students wanting to use SOLVIT at any one time, then
20
0
20
P(X = 0) =
C
(0.2)
(0.8)
= 0.0115
0
20
1
19
P(X = 1) =
C
(0.2)
(0.8)
= 0.0576
1
20
2
18
P(X = 2) =
C
(0.2)
(0.8)
= 0.1369
2
20
3
17
P(X = 3) =
C
(0.2)
(0.8)
= 0.2054
3
20
4
16
P(X = 4) =
C
(0.2)
(0.8)
= 0.2182
4
Therefore
P(X
4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= 0.01152 + 0.0576 + 0.1369 + 0.2054 + 0.2182
= 0.61862
The probability that more than 4 students will want to use SOLVIT is
P(X > 4) = 1
P(X
4) = 0.38138
That is, 38% of the time there will be more than 4 students wanting to use the software. The
Purchasing Department has grossly overestimated the availability of the software on the basis of a
4-user licence.
25
HELM (2008):
Section 37.2: The Binomial Distribution
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