Problem 3.
The average number of thefts at LeBow is three per month. (a)Estimate the probability, p, that at least six thefts occur atLeBow during December. (What inequality are you using?)
(b) Assume now (for parts (b), (c), and (d)) that you are toldthat the variance of the number of thefts at LeBow in any one monthis 2. Now give an improved estimate of p (using an inequality).
(c) Give a Central Limit Theorem estimate for the probability qthat during the next 5 years (12 months per year) there are morethan 150 thefts at LeBow.
(d) Use an inequality to get the best bounds you can on theprobability q estimated in part (c).
