The Hoylake Rescue Squad receives an amergency call every 1, 2, 3, 4, 5, or 6 ho

Question

The Hoylake Rescue Squad receives an amergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution. The squad is on duty 24 hours per day, 7 days per week.

Time between emergency calls                   probability

1                                                                    1.15

2                                                                      0.10

3                                                                     0.20

4                                                                    0.25

5                                                                      0.20

6                                                                      0.10

a. Simulate the emergency calls for 3 days (Note that this will require a runing or cumalative hourly clock), using the random nymber table.

b. Compute the average time between calls and compare this value with the expected value of the time between calls from the probability distribution. Why are the results different?

Explanation / Answer

b.) E(X) =   p*x

= 1*0.15 + 2*0.1 + 3*0.2 + 4*0.25 + 5*0.2 + 6*0.1

= 3.55

Average time between calls =(1+2+3+4+5+6)/6

= 3.5

The results are different because Expected value is weighted average, weighted over the corresponding probability and is a better indicator of the situation.

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