Statistics for Decision- Making in Business - Maricopa Community ...

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This means that, after selling this product for a while, it should earn an average of $103 from each consumer that purchases the warranty. This is a profitable outcome. Example 2: The Arizona Lottery has a number of different lottery games that a person can play. One in particular is Fantasy 5. The rules of the game are simple: pay $1 per ticket and select five numbers between 1 and 41. Five numbers are then selected at random. If you correctly selected two or more of these numbers, then you are considered a winner. The following table describes the likelihood of winning: (SOURCE: www.arizonalottery.com) The estimated jackpot for the Wednesday, August 17, 2011 lottery was $54,000. Is the game in your favor Why or why not SOLUTION: We must first consider the fact that these prizes do not take into account that $1 was lost to purchase the ticket; we should subtract $1 from each of the prizes. Additionally, we note that the probabilities do not add to 1: The remainder of the time, it is simply the case that $1 is lost: We rebuild the table to show all of the values and probabilities: 53,999 499 4 0 -1 ( ) 1/749,398 1/4163 1/119 1/11 9,004/10,000 Statistics for Decision-Making in Business © Milos Podmanik Page 138
Where The expected value is: , - ( ) ( ) ( ) ( ) ( ) This means that if one were to play time-after-time, taking into consideration the small likelihood of winning occasionally, one would be expected to lose, on average, $0.67 per ticket. ’ Notice that we represented the outcomes by using a table, in which we listed the outcomes, or the individual along with the probability that this occurs, ( ). This is one way in which to display a probability distribution, or how all probabilities are distributed among the various outcomes. Example 3: A fair, six-sided die is tossed repeatedly. The number of dots that are facing up after each throw is recorded. Define the random variable, find its probability distribution, and find and interpret the expected value of the random variable. SOLUTION: We define the random variable, The different values that can take on are , since we know there are six sides. Since this is a fair die, each of these six outcomes has an equally likely chance of appearing, so ( ) , for all values, of . Our probability distribution is thus, 1 2 3 4 5 6 ( ) 1/6 1/6 1/6 1/6 1/6 1/6 The expected value is the sum of the products of each outcome value and its associated probability. Statistics for Decision-Making in Business © Milos Podmanik Page 139
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Statistics for Decision- Making in
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A Note to Students This book is far
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6.3 Confidence Interval for ̂ 202
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which has undergone no additional r
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of transporting such an animal. Not
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Although far from last, we will con
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Account Type Revenue ($) New $5,296
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For the present time, we‟ll proce
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Row Labels Average of Revenue ($) M
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(SOURCE: Essentials of Modern Busin
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1.3Statistics in Excel When conduct
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We can make it a bit more presentab
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For measures such as the range, Exc
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We get: We can do the same for Old.
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Chapter 2 Visual Representations of
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We now have to enter a formula for
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We know from the data that this val
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Alternatively, it is possible to in
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16 14 12 10 8 6 Series1 4 2 0 SD D
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Selected the copied graph. In Chart
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2. The following data represents pe
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Frequency 2.2 Visualizing Quantitat
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You can either choose to have Excel
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If we had additional variables, the
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Select PivotChart and select the fi
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Frequency To make solid black lines
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Relative Frequency Histogram of Cal
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a. Using Excel, find the mean and r
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̅ ̅ account for this discrepancy,
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2.3.2 Percentile Another useful too
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2.3.4 Rank What if, on the other ha
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Check the “Analysis ToolPak” an
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You‟ll immediately notice that a
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̅ 2.4 Descriptive Statistics - Var
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√ ∑( ̅) √ √ This is what w
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This gives us a nice measure of how
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We can immediately see the mean and
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Lastly, a normal curve is the most
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Frequency ̅ Histogram of TV's Owne
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58.3 34.6 35.5 45.4 38.6 63.8 53.9
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Chapter 3 Probability and Decision
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Proportion of Rainy Days 1.2 Propor
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This means that if samples of HFCS
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Page 89 and 90: 3.2 Joint Probability In the previo
Page 91 and 92: Company 1 Choices Y Y Y Y Y Y Y Y N
Page 93 and 94: There is less than a 1% chance that
Page 95 and 96: We can now see that the situation i
Page 97 and 98: sequence, one ball is chose at rand
Page 99 and 100: 3.3 Probability of Unions Imagine t
Page 101 and 102: Physical .20 .10 .30 Mental .40 .30
Page 103 and 104: SOLUTION: We first arrange this inf
Page 105 and 106: Homework Problems - 3.3 1. A gaming
Page 107 and 108: 3.4 Conditional Probability In many
Page 109 and 110: ) : The Arizona Cardinals make it t
Page 111 and 112: We could just as well have written,
Page 113 and 114: That is, the probability that the c
Page 115 and 116: This can happen in one of two ways:
Page 117 and 118: f. All numerical red cards are remo
Page 119 and 120: 3.5 Combinations and Permutations R
Page 121 and 122: 1 st Bushel 2 nd Bushel U1 U1 U2 U2
Page 123 and 124: Which, in its final state gives: Th
Page 125 and 126: Combination - Order Does NOT Matter
Page 127 and 128: ( ) There is only a .9% chance that
Page 129 and 130: 1. Are repeats/replacements allowed
Page 131 and 132: Object 4 Object 5 Also notice that
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Page 141 and 142: SOLUTION: We first note that there
Page 143 and 144: Probability 0.7 0.6 0.5 0.4 0.3 0.2
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Page 147 and 148: For men, we see that the most frequ
Page 149 and 150: So, we had 10 trials and wanted to
Page 151 and 152: Example 1: A fair-two sided coin is
Page 153 and 154: ( ) ( ) ( ) ( ) Example 2: A fair,
Page 155 and 156: Expected Value of a Binomial Random
Page 157 and 158: f. What is the probability that g.
Page 159 and 160: Probability For instance, we see th
Page 161 and 162: Density 0.25 Time Speng Waiting in
Page 163 and 164: Suppose we wish to find ( ), that i
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Page 169 and 170: a. What is the probability that the
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Page 173 and 174: As you can see, this is a difficult
Page 175 and 176: We wish to know the area of the sha
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Page 179 and 180: In the second section, we can check
Page 181 and 182: Chapter 6 Sampling Distributions an
Page 183 and 184: Thus, the standard deviation would
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The Central Limit Theorem (CLT) has
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can set this up in our applet by ha
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3) We cannot use this sample to cal
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Thus, we need to find the lower and
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We see that the standard deviation
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√ The lower limit is: √ And the
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following data was collected on the
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{ So, we have a set of twenty 1‟s
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DULY CAUTIONED: The assumptions her
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Homework Problems -6.2 1. In a samp
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Since this is a mathematical questi
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Example 3: Many older homes have el
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Hypothesis Test Conclusion Test Say
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Hypothesis Test Conclusion Since yo
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SOLUTION: d. A generic conclusion s
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9. Based on the “Structure of a H
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1.2 Descriptive VS. Inferential Sta
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Relative Frequency 35% 30% 25% 20%
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Symmetric: 35 30 25 20 15 10 5 0 10
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Repair Cost Mean 971 Standard Error
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el freq Nitrous Oxide (thous. Tons)
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Probability Pizza Size Distribution
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e. ( ) f. ; the average response ti
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2. a. The long-run proportion of al
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e. 20% of all children are expected
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e. The middle 50% score between abo
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5. b. This might indicate that the
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̅ We have that ̅ and √ . So our
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6. This is the probability that we
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