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210HWChapter06

# 210HWChapter06 - a Sample Space 1st Toss what Spot set do...

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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

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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 - μ) (x - μ)^2 (x - μ)^2*P(x) Small \$0.80 0.3 \$0.80 0.3 \$0.24 \$0.80 0.3000 -0.1300 0.0169 0.0051 Medium \$0.90 0.5 \$0.90 0.5 \$0.45 \$0.90 0.5000 -0.0300 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 Σ 0.0201 Σ \$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 15 -0.2 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 all the outcomes into mutually exclusive and collectively 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.

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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)*(x-mu)^2 600 7260 360 2430 150 15210 Mu = Expected Value = 1110 b) Variance 24900 c) Standard Deviation = SQRT(Variance) 157.7973383806 a) Based on past data, we expect 1110 student for the fall semester. c) Based on past data, we have a 68% chance of between 952 students and 1268 students (based on a standard deviation of 158. Check Mu = Expected value = 1110 Check sigma (sD) 157.797338 Check (create formula without brackets and then hold Ctrl and Shift and then tap Enter). This is an Array formula. Array formulas are amongst the hardest and most difficult formulas in Excel to create and understand. The word Array means that calculations are being done on arrays of numbers or cell ranges, instead of just individual numbers or cells. The Ctrl + Shift + Enter tells Excel that you are

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