(5) The potholes on a major Chicago highway occur at an average rate of 3.4 per
ID: 3244050 • Letter: #
Question
(5) The potholes on a major Chicago highway occur at an average rate of 3.4 per mile. Suppose one mile of highway is randomly selected. Use the Poisson table below to answer the following questions:
(a)What is the probability of more than 1 pothole occurring?
14.68%
19.29%
85.32%
96.66%
(b)What is the probability of fewer than 3 potholes occurring?
21.86%
33.97%
44.16%
85.32%
POTHOLES
Data
Average/Expected number of successes:
3.4
Poisson Probabilities Table
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
0
0.033373
0.033373
0.000000
0.966627
1.000000
1
0.113469
0.146842
0.033373
0.853158
0.966627
2
0.192898
0.339740
0.146842
0.660260
0.853158
3
0.218617
0.558357
0.339740
0.441643
0.660260
4
0.185825
0.744182
0.558357
0.255818
0.441643
5
0.126361
0.870542
0.744182
0.129458
0.255818
6
0.071604
0.942147
0.870542
0.057853
0.129458
POTHOLES
Data
Average/Expected number of successes:
3.4
Poisson Probabilities Table
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
0
0.033373
0.033373
0.000000
0.966627
1.000000
1
0.113469
0.146842
0.033373
0.853158
0.966627
2
0.192898
0.339740
0.146842
0.660260
0.853158
3
0.218617
0.558357
0.339740
0.441643
0.660260
4
0.185825
0.744182
0.558357
0.255818
0.441643
5
0.126361
0.870542
0.744182
0.129458
0.255818
6
0.071604
0.942147
0.870542
0.057853
0.129458
Explanation / Answer
Solution:-
a) The probability of more than 1 pothole occurring is 0.8532.
= 3.4
By applying poisons distribution:-
P(x; ) = (e-) (x) / x !
P(x > 1) = 0.8532
The probability of more than 1 pothole occurring is 85.32%.
b) The probability of fewer than 3 potholes occurring is 33.97%.
= 3.4
By applying poisons distribution:-
P(x; ) = (e-) (x) / x!
P(x < 3) = 0.3397
The probability of fewer than 3 potholes occurring is 33.97%.
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