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.