Question

Please answer part d !!! 7.A gambler plays roulette 100 times, betting a dollar on the numbers 1-12 each time. This particular bet pays 2 to 1 (you win $2 if the outcome is a number between 1 and 12 and lose $1 if not), and the chance of winning is 12/38 = 6/19. (You don’t need to know anything more about roulette than is given in this problem to solve it.) Fill in the blanks.(a) In 100 plays, the gambler’s net gain (total amount won or lost) has an expected value of $_____________, with a standard error of $_____________.(b) In 100 plays, the number of times the gambler wins has an expected value of _____________, with a standard error of _____________.(c) If the gambler plays 100 times every month, we can expect that in 95% ofmonths, his net gain will be between $_____________ and $_____________. (d) It ____________ (is OR is not) appropriate to use the normal approximation to calculate the chance of winning on at least 100 out of the 150 plays, because________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________(Your explanation should include the name of a theorem and one or more numerical comparisons.)

Answer 1

We have:

n = 100

p = 12/38 = 6/19 = 0.316

n*p = 100*0.316 = 31.6 5

n*(1 - p) = 100*(1 - 0.316) = 68.4 5

These are both larger than 5, so you can use the normal approximation to the binomial for this question.

It is appropriate to use the normal approximation to calculate the chance of winning on at least 100 out of the 150 plays, because n*p and n*(1 - p) are both larger than 5, so you can use the normal approximation to the binomial for this question.

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