Solve and write in simplest form, 4/6 x 6/8
2 answers:
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Answer:
- Expected Value= -$7
- Bill should not play the game
Step-by-step explanation:
In the game, these are the payout:
- 30% of the time you will lose 20 dollars.
- 20% of the time you lose 40 dollars.
- 10% of the time you win 50 dollars
- 40% of the time you win 5 dollars.
To compute the expected value, take note that a loss is negative while a win is positive.
Therefore:
E(X)=(-20*0.3)+(-40*0.2)+(50*0.1)+(5*0.4)
E(X)=-7
- The expected value of the event is -$7.
- Based on the negative expectation, Bill should not play this game as he is expected to incur a loss.
Using the normal distribution, there is a 0.1894 = 18.94% probability that the sample average will exceed $75.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The parameters for this problem are given as follows:
The probability that the sample average will exceed $75 is <u>one subtracted by the p-value of Z when X = 75,</u> hence:
By the Central Limit Theorem
Z = (75 - 70)/5.66
Z = 0.88
Z = 0.88 has a p-value of 0.8106.
1 - 0.8106 = 0.1894.
0.1894 = 18.94% probability that the sample average will exceed $75.
More can be learned about the normal distribution at brainly.com/question/28096232
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