Question

1. Use the Poisson distribution to approximate the binomial distribution.

b (3; 100, 0.03).

2. In a city 6% of all drivers get al least a fine in a year.

Use the Poisson distribution to approximate the binomial distribution.

Determine the probabilities that between 80 drivers:

a) Al least 4 will get al least one fee in some year;

b) Al least 3 will get al least one fee in some year;

c) Some of them between 3 and 6, considering both values will get al least a fine in a year.

Answer 1

1)

Mean/Expected number of events of interest: λ = 100 * 0.03

= 3

2)

a)

Mean/Expected number of events of interest: λ =                4.8

X	P(X)	P(>X)
0	0.0082
1	0.0395
2	0.0948
3	0.1517	0.7058

b)

X	P(X)	P(>X)
0	0.0082
1	0.0395
2	0.0948	0.8575

c)

X	P(X)
3	0.1517
4	0.1820
5	0.1747
6	0.1398

Probability = 0.6483

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