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Unformatted text preview: Sample Space a) Possible Outcomes 1st Toss what Spot set do we get? P(x) Fraction P(x) Probability P(x) Percent 1 * 1/6 0.1666666667 16.6666667% 2 ** 1/6 0.1666666667 16.6666667% 3 *** 1/6 0.1666666667 16.6666667% 4 **** 1/6 0.1666666667 16.6666667% 5 ***** 1/6 0.1666666667 16.6666667% 6 ****** 1/6 0.1666666667 16.6666667% Count of Possible Outcomes =6 6 Total 1 1 1 b) c) 1 * ** *** **** ***** ****** 0 1/6 P(x) for Possible Outcomes Number of Spots Probability a) This is a discrete probability distribution because you jump from one set price to another. Pizza Palace P(x) P(x) x*P(x) P(x) (x  ) (x  )^2 (x  )^2*P(x) Small $0.80 0.3 $0.80 0.3 $0.24 $0.80 0.30000.1300 0.0169 0.0051 Medium $0.90 0.5 $0.90 0.5 $0.45 $0.90 0.50000.0300 0.0009 0.0004 Large $1.20 0.2 $1.20 0.2 $0.24 $1.20 0.2000 0.2700 0.0729 0.0146 Total 1 Total 1 $0.93 0.0201 $0.93 c) Variance = 0.0201 b) Mu = expected value = $0.93 c) Standard Deviation = 0.1418 c) Three Sizes of Cola: Number of Pennies per cola x Number of Pennies per cola x Number of Pennies per cola x The mean of $0.93 indicates the typical selling price for the cola and the SD indicates that there is variance of 1 SD about the mean of $0.14 on either side of the mean. Approximately 68% of the prices received for cola lie within the range of $0.79 and $1.07. The numbers here are expected values, not actual sale price numbers (because we can't actually sell a cola for $0.93). a) The green cell indicates which table is the Probability Distribution. In this case the sum of the probabilities are equal to 1. x P(x) x P(x) x P(x) 5 0.3 5 0.1 5 0.5 10 0.3 10 0.3 10 0.3 15 0.2 15 0.2 150.2 20 0.4 20 0.4 20 0.4 1.2 1 1 b) 1 P(15) = 0.2 2 P(No more than 10) = P(x <= 10) = 0.4 3 P(More than 5) = P(x > 5) = 0.9 c) x*P(x) P(x)*(x  mu)^2 0.5 =F4*G4 9.025 =G4*(C4$B$24)^2 3 6.075 3 0.05 8 12.1 Mu = expected value = 14.5 Variance 27.25 Standard Deviation 5.2201532545 =SQRT(D24) Sum of all the probabilities must be equal to 1 (because a listing of al the outcomes into mutual y exclusive and col ectively exhaustive categories will yield the associated probabilities that when summed are equal to 1). Probabilities cannot be negative. The definition of probability is that it is a number between 0 and 1, inclusive. Remember, multiplication is commutative (it can be dome in any order). In addition, () and ^ is done before * according to the order of operations. a) Number of new accounts Discrete Discrete b) Time between arrivals Continuous Continuous c) Number of customers Discrete d) Amount of fuel Continuous e) Number of minorities on a jury Discrete f) Temperature Continuous Based On Past Data, An Estimation Of The Distribution Of Student Admissions For Fall Semester Follows: Admissions Probability 1000 0.6 1200 0.3 1500 0.1 1 X*P(x) P(x)*(xmu)^2 600 7260 360 2430 150 15210 Mu = Expected Value = 1110b) Variance 24900 c) Standard Deviation = SQRT(Variance)...
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This note was uploaded on 01/10/2012 for the course BUSN 210 taught by Professor Girvin during the Winter '09 term at Des Moines CC.
 Winter '09
 Girvin

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