James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or loses) per game. The expected value of x, called ux (expected value of x bar) is ________________________ The standard deviation of x (x bar), called 0x (standard deviation of x bar) is _____________________________ this means that for 2500 games, you expect your winnings (or loss) to be 2500 times your average loss per game, which is _____________________. Multiplying the value found for 0x (standard deviation of X (x bar)) by 2500 (the number of games) we find that standard deviation in profit for 2500 games is _________________
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel.
-if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20
-if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150
-if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30
So for each spin; he either wins $150, wins $20, or loses $30
-probability that he wins $150 is 1/38 or .0263
-probability that he wins $20 is 18/38 or .4737
-probability that he loses $30 is 19/38 or .5000
let X = the profit that james makes on the next spin
| x | P (X=x) | x*P(X=x) | x^2*P(X=x) |
| 150 | .0263 | 3.945 | 591.75 |
| 20 | .4737 | 9.474 | 189.48 |
| -30 | .5000 | -15.000 | 450.00 |
| sum (sigma) | 1.000 | -1.581 | 1231.23 |
u (expected value)= -$1.581
variance = 1228.73044
standard deviation = 35.053
FILL IN THE BLANK
if you play 2500 times, and
Let, x (x bar)= the
The standard deviation of x (x bar), called 0x (standard deviation of x bar) is _____________________________
this means that for 2500 games, you expect your winnings (or loss) to be 2500 times your average loss per game, which is _____________________.
Multiplying the value found for 0x (standard deviation of X (x bar)) by 2500 (the number of games) we find that standard deviation in profit for 2500 games is _________________
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