How to find the standard error? please help me. statistic problem.?

Story: A gambler plays roulette and makes a $1 bet on a pair of numbers 4000 times. The bet pays 17 to 1, and it covers two numbers. We are interested in finding the chance that the casino will make less than $300 from these plays.





Find the standard error or the sum.


a. 254.21


b. 56.76


c. 35.90


d. 4.71


e. none of these

How to find the standard error? please help me. statistic problem.?
reduce this to probabilities.


prob of winning $17 (you put down 1 and they give back 18)


is 2/38.....2 numbers out of the 38 possible on the wheel.


prob of losing $1 is 36/38.





You need to be able to compute expectations for discrete random variables.


Expectation of gain on one trial=(2/38)*17+(36/38)*(-1)


=-$(1/19) one-nineteenth of a dollar.


On 4000 trials your expection is -4000/19=-$210.53


You will expect to be $210 in the hole.





What is the probability of being more than $300 in the hole?


You need the standard error associated with the mean.





variance on one trial=


(2/38)* ( 17 + 1/19)^2 + (36/38)*(-1+ 1/19)^2 = 16.154





multiply by 4000^2, take the square root, divide by sqrt(4000) . getting $ 254.2 = SE





-300 is 89.47 lower than the mean of 210,


or z=-0.35=89.47/254.20





looks like 36.32% is the probability (0.3632) of the gambler losing more than $300. OR 63.68% for the casino gaining less than $300.





So, the SE is (a)


and the prob that the casino makes less than $300 is 0.6368.