Suppose that the average number of parking tickets given in front of a store is

Question

Suppose that the average number of parking tickets given in front of a store is three per day.

(a) Estimate the probability, p, that at least five parking tickets will be given out in front of the store tomorrow. (What inequality are you using?)

(b) Assume now (for parts (b), (c), and (d)) that you are told that the variance of the number of tickets in any one day is 9. Now give an estimate of p that takes advantage of knowing the variance (using an inequality).

(c) Give a Central Limit Theorem estimate for the probability q that in the month of December (which has 31 days, and we consider each day to be like any other day) there are more than 75 parking tickets given out.

(d) Use an inequality to get the best bounds you can on the probability q estimated in part (c).

Explanation / Answer

X: No of vehicles parking tickets given in front of a store is Poisson with mean = 3

a) P(atleast 5 vehicles) = P(X>=5) = 0.1847

b) Given that mu=3 and variance = 9

For 31 working days average= 31*3 =93
P(X>75) = P(x-mu>18)

=P(x-mu >2 sigma) = 1/(4*2) =0.125

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