1. ## Normal Distribution

I have a statistics problem I can’t solve for some reason:

A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average bet of $50. The player’s strategy provides a probability of .49 of winning on any one hand, and the player knows that there are 60 hands per hour. Suppose the player plays for four hours at a bet of$50 per hand.

b. What’s the probability the player loses $1000 or less? Answer: .1788 For some reason I can’t get their answer. It looks like a really simple normal approximation of binomial probabilities question, but for some reason none of my answers turn out right. I got the expected value of this game as -240, because he wages$12,000 total and the difference between his expected winnings and expected losses is -240.

This is the part where I don’t know how I went wrong: I found standard deviation using sqrt(12000*.49*(1-.49)), which is from sqrt(n*p*(1-p)). It’s 54.7613

Next, I find the z-score, which comes out as -13.8689. I got this using z=(x-u)/s

-13.8689 is so high of a z value it’s not even on my chart. What did I do wrong?

2. Originally Posted by lisakki
I have a statistics problem I can’t solve for some reason:

A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average bet of $50. The player’s strategy provides a probability of .49 of winning on any one hand, and the player knows that there are 60 hands per hour. Suppose the player plays for four hours at a bet of$50 per hand.

b. What’s the probability the player loses $1000 or less? Answer: .1788 For some reason I can’t get their answer. It looks like a really simple normal approximation of binomial probabilities question, but for some reason none of my answers turn out right. I got the expected value of this game as -240, because he wages$12,000 total and the difference between his expected winnings and expected losses is -240.

This is the part where I don’t know how I went wrong: I found standard deviation using sqrt(12000*.49*(1-.49)), which is from sqrt(n*p*(1-p)). It’s 54.7613

Next, I find the z-score, which comes out as -13.8689. I got this using z=(x-u)/s

-13.8689 is so high of a z value it’s not even on my chart. What did I do wrong?
Let X be the random variable number of games won.

X ~ Binomial(n = 240, p = 0.49)

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