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2. [4 marks] Question 15.40. It is said that the New York City mobster Casper Holstein
took as many as 25,000 bets per day in the Prohibition era. That's 150,000 bets in a week
if he takes Sunday off. Casper's mean winnings per bet are $0.40. His standard deviation
for single bets is about $18.96.
3 a. What are the mean and standard deviation of Casper's average winnings ã on his
150,000 bets? [2 marks]
b. According to the central limit theorem, what is the approximate probability that Casper's
average winnings per bet are between $0.30 and $0.50? After only a week, Casper can be
pretty confident that his winnings will be quite close to $0.40 per bet. [2 marks]
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