Can you help with my statistics question
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Can you help with my statistics question

[From: ] [author: ] [Date: 11-05-14] [Hit: ]
Find the chance that the casino will make less than $300 from these plays.So far,Expected Value: $210.Standard Error for Sum: $254.I know that these are correct.I also worked out the average to be .......
Hi, the question is:
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. (*note, there are 38 spaces on a roulette wheel)
Find the chance that the casino will make less than $300 from these plays.

So far, I've found:
Expected Value: $210.53
Standard Error for Sum: $254.21
I know that these are correct.

I also worked out the average to be .0625. No confirmation on whether that is correct or not, but I'm pretty sure that it is correct.
I'm trying to find the z value for the normal curve. And I came up with
z1 = 300 - (-.0625)
___________
254.21 = 1.18

That spot on the normal curve occupies 76.99% of the curve from -1.18 to + 1.18.
So I subtracted that percentage from 100% (23.01%), split the answer in half (11.51%), and then added it to half of 76.99% (38.5%+11.51%) because that SHOULD be the correct area of the curve that is less than $300. The answer as I have it worked out to 50%, but the correct answer according to the answer key is 63.69%. What did I do wrong?
How do you work this properly? I know how to find an area between two points on the normal curve, and I've done that without problem, but this I can't figure out! HELP! My test is on Sunday, and I need to know how to work this.
Thanks!

-
I have not understood the situation perfectly. But still let me say that
Z = (300-210.53)/254.21 = 0.35.
P[X<300] = P[Z<0.35] = 0.5+0.1369 = 0.6369
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