In a lottery, you bet on seven-digit number between 0000000 and 1111111. For a $1 bet, you
Question:
In a lottery, you bet on seven-digit number between 0000000 and 1111111. For a $1 bet, you win $500,000 if you are correct. The mean and standard deviation of the probability distribution for the lottery winnings are u=0.05 (that is,5 cents) and σ=200.00 Joe figures that if he plays enough times every day, eventually he will strike it rich, by the law of large numbers. Over the course of several years, he plays 1 million times.
Let x denote his average winnings.
a. Find the mean and standard deviation of the sampling distribution of x
b. About how likely is it that Joe's average winnings exceed $1, the amount he paid to play each time?
Use the central limit theorem to find an approximate answer.
Statistics The Art and Science of Learning from Data
ISBN: 978-0321755940
3rd edition
Authors: Alan Agresti, Christine A. Franklin