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c) The expected value is, , - ( ) . Thus, we expect that each hour 4 out of 10 homeowners accept the maintenance offer. Homework Problems –4.1 1. Determine whether or not each of the following experiments represents a binomial experiment. (Video Solution) a. A die is rolled 20 times and the number of 6‟s is counted. b. A die is rolled until ten 6‟s show up. c. In a stream with 1,500 fish, 700 are Rainbow Trout. A total of 20 fish are caught and the number of Rainbow Trout is counted. d. About 10% of the U.S. population is suspected to have a form of bacteria. A sample of 100 people is drawn from the population and the number of people with the strain of bacteria is counted. e. A brand of LED light bulb has a 0.5% chance of going out prior to the advertised life of 30,000 hours. In the testing phase, 850 bulbs are sampled for quality assurance. The number of bulbs that don‟t die prior to the 30,000 hour life is counted. 2. Suppose the outcome of random variable is conducted with trials each with independent probability of success, . (Video Solution) a. Is this a binomial experiment b. What is the probability that c. What is the probability that d. What is the probability that e. What is the probability that Statistics for Decision-Making in Business © Milos Podmanik Page 156
f. What is the probability that g. What is , - Does it coincide with the resulting that has the highest probability 3. In preparing for a New Year‟s Eve celebration, police look at past records for arrests due driving under the influence (DUI). In the U.S., 10.5% of arrests made are for DUI (SOURCE: U.S. Statistical Abstract, Table 324). If it is expected that each police officer makes 10 arrests, what is the probability that all arrests result in DUI‟s (Video Solution) 4. Pancreatic cancer is a vicious killer. The 5-year survival rate between 2001 and 2007 was only 5.9%, meaning that the majority of people with pancreatic cancer die within 5-years of contracting the cancer. In a group of 25 patients, 5 survive beyond. How likely is such an event Assume that the survival of one person is independent of another person. (SOURCE: U.S. Statistical Abstract, Table 182). (Video Solution) 5. A new herbal drink blend is being compared to an older blend via a blind taste-test comparison. Four judges will taste each of the two drinks and will state their preference. It is anticipated that both blends are equally impressive. (Video Solution) a. Find the probability distribution for the number of judges that vote in favor of the new blend. b. Construct a probability histogram. c. What is the probability that at least two of the judges prefer the new blend d. What is the expected value of this distribution and what is its real-world meaning 6. Goranson and Hall (1980) explain that the probability of detecting a crack in an airplane wing is the product of , the probability of inspecting a plane with a wing crack; , the probability of inspecting the detail in which the crack is located; and , the probability of detecting the damage. (Problem Source: Mathematical Statistics with Applications, 6 th Ed., Wackerly, et. al.) (Video Solution) a. What assumptions justify the multiplication of these probabilities b. Suppose and for a certain fleet of planes. If three planes are inspected from this fleet, find the probability that a wing crack will be detected on at least one of them. c. Find the probability distribution for the number of planes in this fleet with detected wing cracks. d. Construct a probability histogram. e. What is the expected value of this distribution and what is its real-world meaning Statistics for Decision-Making in Business © Milos Podmanik Page 157
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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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Are we confident in accusing a lung
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3.2 Joint Probability In the previo
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Company 1 Choices Y Y Y Y Y Y Y Y N
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There is less than a 1% chance that
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We can now see that the situation i
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sequence, one ball is chose at rand
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3.3 Probability of Unions Imagine t
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Physical .20 .10 .30 Mental .40 .30
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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
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: Expected Value of a Binomial Random
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
Page 183 and 184: Thus, the standard deviation would
Page 185 and 186: 1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
Page 187 and 188: 2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
Page 189 and 190: The Central Limit Theorem (CLT) has
Page 191 and 192: can set this up in our applet by ha
Page 193 and 194: 3) We cannot use this sample to cal
Page 195 and 196: Thus, we need to find the lower and
Page 197 and 198: We see that the standard deviation
Page 199 and 200: √ The lower limit is: √ And the
Page 201 and 202: following data was collected on the
Page 203 and 204: { So, we have a set of twenty 1‟s
Page 205 and 206: 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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