Question

Note: Use statistical tables when it is possible The number of accidents at an intersection follows Poisson distribution with an average of three accidents per day. Find (Round to THREE decimal places) 1. The probability of an accident-free day. 2. The probability that there is at most 14 accidents in five days. 3. The accepted number of accident-free days in January 4. The probability that there are four accident-free days in January Calculate \mu and \sigma 2 ? 5. Suppose you are interested in two accident-free days, what is the probability that you should wait for exactly 10 days to count two accident-free days?

Answer 1

1) probability of an accident-free day =P(X=0)=e^-3*3⁰/0! =0.050

2)

e probability that there is at most 14 accidents in five days =P(X<=14)==0.466

3)

The accepted number of accident-free days in January =np=31*0.050=1.55

4)

=1.55 ( please try 1.543 if this comes wrong)

² =1.55 (please try 1.543 if this comes wrong)

5)

probability that you should wait for exactly 10 days to count two accident-free days

=P(till 9 days 1 accident free day and on 10th day we get 2nd accident free day)

= =0.015