Tom is involved in a risky enterprise that, if it succeeds, will net him $100. I
ID: 3179865 • Letter: T
Question
Tom is involved in a risky enterprise that, if it succeeds, will net him $100. If it does not, he will lose his initial investment of $7. The probability of success is estimated to be 0.20 (20%).
The expected value of this investment is $Answer. (to the nearest cent. no dollar signs or commas)
Continuing from the previous question, an investment offers a $100 GAIN with probability 0.20 and a $7 LOSS with a probability of 0.80.
What is the variance of the net gain from this investment? Answer
(no dollar signs or commas)
Continuing, the standard deviation of the net gain from this investment would be
± $ Answer (two decimal places. no commas or dollar signs)
Injury accidents at a certain traffic intersection occur randomly at the mean rate of 2.9 per month.
How many accidents would be expected in the next five months? Give your answer to at least one decimal place.
Answer accidents in a five-month period
Continuing from the previous question, what's the probability that exactly eight accidents will occur in the next five months?
Answer (to at least 4 decimal places)
Continuting from the previous two questions, if X = the number of injury accidents at this intersection in a five month period, what is the variance of X?
Answer (to at least one decimal place)
In your experience as a tax accountant, 45% of the taxpayers in a certain category get audited by the IRS every year, chosen more or less at random. You have 12 clients in this category. Let A = the number of these clients that get audited.
What is the expected value of A? Answer (two decimal places)
Continuing, what is the standard deviation of the random variable A?
Answer (to at least two decimal places)
Continuing, what's the probability that at least one of the twelve clients you have in this category will be audited by the IRS?
Answer (at least four decimal places)
Continuing, what is the probability that exactly three of your clients will be audited by the IRS?
Answer (at least four decimal places)
Continuing, what's the probability that fewer than three of these twelve clients will be audited by the IRS?
Answer (to at least four decimal places)
Continuing, what's the probability that at least three of the twelve clients will be audited by the IRS?
Answer (to at least four decimal places)
Explanation / Answer
(a) Expected value of investment will be : 100*.2 -7*.8 = 14.4
(b) Let X denote the payoff from the investment , then E( X2 ) = 1002 *.2 +(-7)2 * .8 = 2039.2 , variance is -
E( X2 ) - [E( X)]2 = 2039.2 - 14.42 = 1831.4
(c) and (d) Let Y denote the number of accidents ocurring in one month period, then Y follows poisson distribution with mean = 2.9
Then over the five month period, total number of accidents must have poisson distribution with mean = 2.9*5 = 14.5
and variance = 2.9 + 2.9+2.9+2.9+2.9 = 14.5 ( because number of accidents in different months are independent). X denoting the total number of accidents over five month timr period must follow poisson with parameter equal to 14.5
P(exactly 8 accidents in next five months ) = (14.5)8 e-14.5 / 8! = .024443
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