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

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Suppose that an emergency room in New York City has two individuals with flu-like symptoms. (Video Solution) a. What condition(s) do you believe would make it appropriate to assume independence in this situation b. By using the tabular approach and assuming independence, find the probability that both people have the H1N1 virus. c. By using the “and” rule, verify that you get the same answer that you found in Part b. d. Find the probability that neither of these individuals has the H1N1 virus. e. Find the probability that at least one of them has the H1N1 virus. f. Exposure to flu germs for even a short period of time can significantly increase one‟s chances of catching the flu. Suppose that if one is exposed to an individual with the flu virus, their chance of becoming infected is 15 percentage points higher than normal. Find the probability that both individuals have the flu virus. 2. Many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. A particular station says that the probability that an incoming call is for medical assistance is .85. This can be expressed as P(call is for medical assistance) = .85. a. Give a relative frequency interpretation of the given probability. That is, interpret what the number .85 means based on the definition of probability. b. What is the probability that a call is not for medical assistance c. Assuming that successive calls are independent of one another (i.e., knowing that one call is for medical assistance doesn't influence our assessment of the probability that the next call will be for medical assistance), calculate the probability that both of the two successive calls will be for medical assistance. d. Still assuming independence, calculate the probability that for two successive calls, the first is for medical assistance and the second is not for medical assistance. e. Still assuming independence, calculate the probability that exactly one of the next two calls will be for medical assistance. (Hint: There are two different possibilities that you should consider. The one call for medical assistance might be the first call, or it might be the second call.) f. Do you think it is reasonable to assume that the requests made in successive calls are independent Explain. 3. "N.Y. Lottery Numbers Come Up 9-1-1 on 9/11" was the headline of an article that appeared in the San Francisco Chronicle (September 13, 2002). More than 5600 people had selected the sequence 9-1-1 on that date, many more than is typical for that sequence. A professor at the University of Buffalo is quoted as saying, "I'm a bit surprised, but I wouldn't characterize it as bizarre. It's randomness. Every number has the same chance of coming up. People tend to read into these things. I'm sure that whatever numbers come up tonight, they will have some special meaning to someone, somewhere." The New York state lottery uses balls numbered 0-9 circulating in 3 separate bins. To select the winning Statistics for Decision-Making in Business © Milos Podmanik Page 96
sequence, one ball is chose at random from each bin. What is the probability that the sequence 9-1-1 would be the one selected on any particular day 4. On August 8, 2011, the Dow Jones Industrial fell 635 points (5.5%) to 10,810 points, representing the 6 th worst point loss ever experienced. On that day, President Obama‟s approval ratings also suffered tremendously; only 22% of the nation‟s voters “Strongly Approve” of how he is performing in the presidential role (SOURCE: http://www.rasmussenreports.com/public_content/politics/obama_administration/daily_pr esidential_tracking_poll). Suppose presidential hopeful Randall Terry (Democrat) speaks at a rally shortly thereafter and assumes that his approval rating as a candidate will likely closely mirror President Obama‟s. Suppose there are 40 swing voters (voters that are “on the fence” about who to vote for). (Video Solution) a. What is the probability that all 40 voters will strongly approve of Terry‟s plan b. What is the probability that none of the 40 voters will strongly approve of Terry‟s plan c. What is the probability that at least one voter will approve of Terry‟s plan 5. The following case study is reported in the article "Parking Tickets and Missing Women," which appears in an early edition of the book Statistics: A Guide to the Unknown. In a Swedish trial on a charge of overtime parking, a police officer testified that he had noted the position of the two air valves on the tires of a parked car: To the closest hour, one valve was at the 1 o' clock position and the other was at the 6 o' clock position. After the allowable time for parking in that zone had passed, the policeman returned, noted the valves were in the same position, and ticketed the car. The owner of the car claimed that he had left the parking place in time and had returned later. The values just happened by chance to be in the same positions. An "expert" witness computed the probability of this occurring as (1/12)(1/12) = 1/144. a. What reasoning did the expert use to arrive at the probability of 1/144 b. Can you spot the error(s) in the reasoning that leads to the stated probability of 1/144 What effect does this error(s) have on the probability of occurrence Do you think that 1/144 is larger or smaller that the correct probability of occurrence 6. Jeanie is a bit forgetful, and if she doesn't make a "to do" list, the probability that she forgets something she is supposed to do is .1. Tomorrow she intends to run three errands, and she fails to write them on her list. a. What is the probability that Jeanie forgets all three errands What assumptions did you make to calculate this probability b. What is the probability that Jeanie remembers at least one of the three errands c. What is the probability that Jeanie remembers the first errand but not the second or third 7. One of the myths most commonly believed by students on multiple choice exams is that, as long as they always use letter „C‟ as their guess, they increase their chances of Statistics for Decision-Making in Business © Milos Podmanik Page 97
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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
Page 45 and 46: You can either choose to have Excel
Page 47 and 48: If we had additional variables, the
Page 49 and 50: Select PivotChart and select the fi
Page 51 and 52: 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: We can now see that the situation i
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
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
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For men, we see that the most frequ
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So, we had 10 trials and wanted to
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Example 1: A fair-two sided coin is
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( ) ( ) ( ) ( ) 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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