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# Probability Distribution for Traffic Accidents

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The follow table contains the probability distribution for the number of traffic accidents daily in a small city.
See attached.
a. Compute the mean number of accidents per day.
b. Compute the standard deviation.

#### Solution Preview

See the attached file.

5.2
X P(X) X.P(x) [X - m] [X - m]2 P(X)*[X - m]2
0 0.1 0.00 -2.00 4.00 0.40
1 0.2 0.20 -1.00 1.00 0.20
2 0.45 0.90 0.00 0.00 0.00
3 0.15 0.45 1.00 1.00 0.15
4 0.05 0.20 2.00 4.00 0.20
5 0.05 0.25 3.00 9.00 0.45
m = 2.00 1.40
Mean = 2.0
Standard deviation = 1.18

5.1 n = 5
p = 0.4
P(X)

P(X = 4) = 5! (0.4)4 (1-0.4)5-4
4!(5-4)!
P(X = 4) = 5*0.4*0.4*0.4*0.4*0.6= 0.077

P(X<=3)= P(X=0) + P(X = 1) + P(X=2)+P(X=3)

P(X=0) = 5! (0.4)0 (1-0.4)5-0 0.07776
0!(5-0)!

P(X = 1) = 5! (0.4)1 (1-0.4)5-1 0.2592
1!(5-1)!

P(X=2) = 5! (0.4)2 (1-0.4)5-2 0.3456
2!(5-2)!

P(X=3) = 5! (0.4)3 (1-0.4)5-3 0.2304
3!(5-3)!

P(X<=3) = 0.91296

P(X<2) = P(X=0) + P(X=1)
P(X<2) = 0.33696

P(X>1) = 0.07776

5.15 Mean = np = 20*0.05 = 1
a Standard ...

#### Solution Summary

Solution to multiple statistics problems. The expert examines probability distribution for traffic accidents.

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