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

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Object 2 Object 3 Object 4 Object 5 OBJECT 3 Object 1 Object 2 Object 3 Object 4 Object 1 Object 2 Object 3 Object 4 Object 5 Now, notice that we have 10 white spots left. This happens to be exactly one-third of what we had after we tripled the table. That is, ⏟ ⏟ Which can be simplified to, ( ) Selecting items allows this process to repeat, ad nauseam, any number of times. Mathematicians discovered that this tabular process could be reduced into the formula we “ ” general case (where we allow to be any value between 0 and the number of items we have to choose from), which tends to be discussed in more theoretical mathematics courses such as Discrete Mathematical Structures (our MAT227). Homework Problems - 3.5 1. If possible, give an imaginary (but realistic) scenario for each of the following. If not possible, state why. a. b. c. d. Statistics for Decision-Making in Business © Milos Podmanik Page 132
e. 2. Your classmate was absent when permutations and combinations. Explain when he should and when he should not use permutations and combinations. (Video Solution) 3. A police officer has been brought before the court on accusations of racial profiling. This occurs when a person of a particular race has been pulled over or detained by the police due to his race. The officer stopped 2 vehicles out of 10 that passed by through a freeway tollbooth. Both of the suspects were Asian and there were a total of 3 Asian drivers in the 10. (Video Solution) a. In how many ways could 2 drivers have been selected from the 10 b. In how many ways could 2 Asian drivers have been selected from the 3 c. How likely is it that the 2 selected drivers would both have been Asian if the stops were truly random 4. In the United States, 20 out of the 50 states spend more than 50% of their state park and recreation areas revenue on keeping the state park operable (SOURCE: 2012 U.S. Statistical Abstract). Suppose a survey of 10 states is to be conducted next year to see if anything has changed. (Video Solution) a. In how many ways can 10 states be selected for the survey b. In how many ways can 10 states be drawn so that all 10 are operating on more than 50% of their state park and recreation areas revenue c. What is the probability that all 10 of the states drawn are operating on more than 50% of their state park and recreation areas revenue 5. Ten pieces of furniture are to be arranged in a long row in a furniture store. In how many ways can all 10 be arranged (Video Solution) 6. At Chandler-Gilbert Community College high-school math competitions, students enter into a raffle to win various prizes, including a graphing calculator. There are typically around 200 students. Suppose there are 5 different types of calculators to be given out and that the best is saved for last. (Video Solution) a. In how many ways can the prizes be distributed among the 200 students b. Suppose a school has 5 attendees. In how many ways can all 5 students from this school win a calculator c. What is the probability that all 5 students from this school wins a calculator 7. A frequent concern of cautious consumers is the idea of the last four digits of a credit card number being displayed on receipts. Suppose a consumer has a Visa, which has a total of 16-digits, each of which can be between 0 and 9. For the sake of simplicity, suppose any combination is possible. A customer left the following receipt lying around and is now concerned about his identity: (Video Solution) Statistics for Decision-Making in Business © Milos Podmanik Page 133
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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
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 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: Object 4 Object 5 Also notice that
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,
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
Page 165 and 166: Density Resulting in a standard dev
Page 167 and 168: Density Without going into detail h
Page 169 and 170: a. What is the probability that the
Page 171 and 172: Statistics for Decision-Making in B
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
Page 177 and 178: We can easily find that the probabi
Page 179 and 180: In the second section, we can check
Page 181 and 182: 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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