STAT2103 Business statistics
P1: A game has the following probabilities of winning certain dollar amounts. There is a 10% chance you will win $5 and a 40% chance you will win $7 and 50% chance that you will win only $3. However, to play a game, you must pay $5 for each play. Answer the following questions:
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Write the probability model for the total net winnings.
Answer: Net winnings (X) = winnings – payment
X |
0 |
2 |
-2 |
P |
0.1 |
0.4 |
0.5 |
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What type of random variable net winnings is? Answer: Discrete
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What are the mean and standard deviation of total net winnings?
Answer: Mean__-.2_ and Stdev._1.8868_.
You play the above game twice. Assume both plays are independent.
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What is the mean of your total winnings?
Answer: Mean _2*(-.2) = -.4___
P2: A multiple choice test has 50 independent questions. Suppose you have 70% chance of getting each question right. Let X be the # of right answers. Answer the following questions:
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What is P(X 30)? Answer:_.08480____
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What is P(X40)? Answer:__.0788______
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What is P( 30 X 40)? Answer:__.9120__
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What are the mean and standard deviation of X? Answer: Mean_35_ and Stdev. 3.24.
P3: The rate of return (ROR) from a mutual fund is normally distributed with mean 6% and standard deviation 1.2%. Answer the following:
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What is P(ROR4.5%)? Answer:_.1056____
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What is P(ROR7.5%)? Answer:__.1056___
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What is P(4.5% ROR 7.5%)? Answer:__.7887___
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Calculate the lower 5 percentile of ROR. Answer:__4.026___
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Calculate the upper 5 percentile of ROR. Answer:__7.973__
P4: CO emissions for a certain car vary with mean 3 g/mi and standard deviation 0.5g/mi. A company has 80 of these cars in its fleet. Let represent the mean CO level for the company fleet.
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What is the name of the approximate probability distribution of ? Hint: Check the CLT definition. Answer: is approximately N(3, .0559)
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What is P(< 3.1 g/mi)? Answer:_0.963___
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If the number cars in the fleet increase to 320, what happens to the answer in question 14?
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Answer: is approximately N(3, .0279) => standard deviation of the decreases ½ of the answer in 14 and the normal approximation gets better!
P5: How much money do winners go home with from the TV show Jeopardy? A random sample of 15 winners was drawn and their total dollar winnings were given below:
26650
6060
52820
8490
13660
25840
49840
23790
51480
18960
990
11450
41810
21060
7860
Answer the following questions:
Note: n=15, =24050.67 and s =17386.13
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The margin error of 95% confidence interval of mean winnings? Answer:_9628__
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The L and U of 95% confidence interval of mean winnings?
Answer: L = 14423 and U = 33679
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Explain the meaning of above 95% CI in plain English.
Answer: 95% confident that the unknown mean winnings falls in between 14423 and 33679. Formally it says “ 95% of samples of this size (n=15) will produce confidence intervals that capture the true mean”.
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