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

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We find that there is a 62.5% chance that in a couple either the husband votes Republican, the wife votes Republican, or both vote Republican. At this point you might be wondering why we don‟t simply draw out the table and ignore the mathematical formulas. When possible, tables are extremely useful, but they might not always be available. Consider the following example. Example 3: Testing has determined that a particular ballistic missile has an 80% chance of hitting its intended target. Suppose that an enemy jet approaches a military base and so two missiles are fired at the incoming jet. What is the probability that this threat is eliminated SOLUTION: This is the probability that one or both missiles hit the target. We only have one probability, so filling out a table would not be possible. Let We want to know ( ) ( ) ( ) ( ) We already know the first two probabilities on the right hand-side (.80), but we are not given information on ( ). We can fairly assume that the outcome of one missile has no (or very minimal) impact on the outcome of another missile, and so we assume the events are independent. This allows us to write: ( ) ( ) ( ) And so, ( ) We conclude that there is a 96% chance that the enemy jet is eliminated. Statistics for Decision-Making in Business © Milos Podmanik Page 104
Homework Problems - 3.3 1. A gaming investor is considering becoming a financial partner in a new casino. In deciding to go in on the deal, he reviews gaming revenues for previous years. From experience and industry research, he decides that the gaming industry tends to be successful when total gross revenues for card rooms are above $1 million or when gross revenues for lotteries are above $20 billion. Between 2000 and 2009, he found that 50% of the time, both sectors have been successful and that 0% of the time only card tables were successful (and lotteries were not). Lotteries were unsuccessful 30% of the time (SOURCE: 2011 U.S. Statistical Abstract, Table 1258). What is the probability that the investor‟s conditions will be met In your professional opinion, is it likely that he will decide to become a partner in the proposal (Video Solution) 2. A researcher conducts a study on a total of 600 cats to determine whether or not they tend to be adaptive to danger and whether or not their time to respond to those dangers is fast enough to avoid harm. The animals were exposed to non-harmful stimuli to assist in answering the researcher‟s questions. In his report he details that, “207 non-adaptive cats were studied and, of them, 180 were found to have response times that were simply not fast enough. By comparison, a total of 300 cats were both adaptive and had response times that were fast enough.” How likely is it that a cat is adaptive to environmental physical dangers or has a response time that is fast enough (Video Solution) 3. In the March 3, 2011 episode of the Dr. Oz Show entitled “Dangerous Doctors: Is Your MD Hazardous to Your Health” Dr. Oz mentioned that 20% of the time doctors order scans to protect themselves from a lawsuit. Dr. Oz also said, “Up to 1/3 of all tests and treatments are entirely unnecessary.” (Video Solution) a. Two patients are given orders for scans from a particular doctor. What is the probability that one patient or the other were given scans to protect the doctor against a lawsuit b. One patient is given orders for two different tests/treatments. What is the probability that one or both of them was/were unnecessary c. A patient is prescribed a scan and a blood test. What is the probability that an unnecessary prescription was made, through the patient‟s eyes 4. In all of his Fall 2010 classes, Milos discovered that 44% of his students earned a „B‟ or better on their homework average. He also discovered that 50% of his students had a „B‟ or better homework average or a „B‟ or better overall grade in the class (SOURCE: Milos‟ Fall 2010 Grade Spreadsheet). If 30% of all his students received a „B‟ or better homework average and a „B‟ or better class grade, what percentage of his students earned a „B‟ or better in the class (Video Solution) 5. In all of his Fall 2010 classes, Milos discovered that the percentage of all students that earned a „C‟ or better homework average, 87% of these students earned a „C‟ or better final class grade. 70% of all students in his classes earned a „C‟ or better homework average or earned a „C‟ or better final class grade (SOURCE: Milos‟ Fall 2010 Grade Spreadsheet), while only 49% earned a „C‟ or better on homework and as a final class Statistics for Decision-Making in Business © Milos Podmanik Page 105
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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
Page 53 and 54: Relative Frequency Histogram of Cal
Page 55 and 56: a. Using Excel, find the mean and r
Page 57 and 58: ̅ ̅ account for this discrepancy,
Page 59 and 60: 2.3.2 Percentile Another useful too
Page 61 and 62: 2.3.4 Rank What if, on the other ha
Page 63 and 64: Check the “Analysis ToolPak” an
Page 65 and 66: You‟ll immediately notice that a
Page 67 and 68: ̅ 2.4 Descriptive Statistics - Var
Page 69 and 70: √ ∑( ̅) √ √ This is what w
Page 71 and 72: This gives us a nice measure of how
Page 73 and 74: We can immediately see the mean and
Page 75 and 76: Lastly, a normal curve is the most
Page 77 and 78: Frequency ̅ Histogram of TV's Owne
Page 79 and 80: 58.3 34.6 35.5 45.4 38.6 63.8 53.9
Page 81 and 82: Chapter 3 Probability and Decision
Page 83 and 84: Proportion of Rainy Days 1.2 Propor
Page 85 and 86: This means that if samples of HFCS
Page 87 and 88: Are we confident in accusing a lung
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: SOLUTION: We first arrange this inf
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
Page 133 and 134: e. 2. Your classmate was absent whe
Page 135 and 136: 3.6 Expected Value Imagine that you
Page 137 and 138: An expected value is actually not s
Page 139 and 140: Where The expected value is: , - (
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
Page 145 and 146: Statistics for Decision-Making in B
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,
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Expected Value of a Binomial Random
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f. What is the probability that g.
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Probability For instance, we see th
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Density 0.25 Time Speng Waiting in
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Suppose we wish to find ( ), that i
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Density Resulting in a standard dev
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Density Without going into detail h
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a. What is the probability that the
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Statistics for Decision-Making in B
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As you can see, this is a difficult
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We wish to know the area of the sha
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We can easily find that the probabi
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In the second section, we can check
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Chapter 6 Sampling Distributions an
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Thus, the standard deviation would
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1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
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2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
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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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