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  3. in a​ lottery, you bet on a six-digit numbe

In a​ lottery, you bet on a six-digit number between 000000 and 111111. For a​ $1...

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Statistics

In a​ lottery, you bet on a six-digit number between 000000 and111111. For a​ $1 bet, you win ​$700,000 if you are correct. Themean and standard deviation of the probability distribution for thelottery winnings are μ=0.70 (that is, 70 cents) and σ=700.00. Joanfigures that if she plays enough times every​ day, eventually shewill strike it​ rich, by the law of large numbers. Over the courseof several​ years, she plays 1 million times. Let x denote heraverage winnings.

a. Find the mean and standard deviation of the samplingdistribution of x

b. About how likely is it that Joan​'s average winnings exceed​$1, the amount she paid to play each​ time? Use the central limittheorem to find an approximate answer.

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