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

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We assume that each parent is equally likely to give either of the two alleles and that, if either one or two of the alleles in a pair is dominant (R), the offspring will have red flowers. (Problem source: Mathematical Statistics with Applications, 6 th Ed., Wackerly, et al.) (Video Solution) a. What is the probability that an offspring has one recessive allele, given that the offspring has red flowers b. What is the probability that an offspring has one dominant allele, given that the offspring has white flowers c. What is the probability that an offspring has white flowers, given that it has one recessive allele d. What is the probability that an offspring has white flowers, given that it has one dominant allele e. What is the probability that an offspring has red flowers, given that it has one dominant allele 5. There are 5 candidates for 2 town council positions. Three of them are for the removal of a landfill just outside of the city limits. The same candidate cannot fill both seats. (Video Solution) a. What is the probability that one randomly chosen candidate in the group is for the removal of the landfill b. Given that one of the positions is filled with a candidate in favor of the landfill removal, what is the probability that the second candidate chosen is also in favor c. What is the probability that two candidates in favor of the landfill removal are chosen d. What is the probability that only one seat is filled by a candidate in favor of the landfill removal e. What is the probability that at least one seat is filled by a candidate in favor of the landfill removal Statistics for Decision-Making in Business © Milos Podmanik Page 118
3.5 Combinations and Permutations Recall from Section 3.2 the problem faced by a corn growing business: the FDA determines that two of the 20 bushels are potentially contaminated with E. coli. Two bushels had been shipped out and the question was: what is the probability that both bushels that were shipped to the local grocer were uncontaminated We wrote the simultaneous probability as ( ) ( ) ( ) Due to the fact that one of the uncontaminated bushels was removed from the “pool”, there was now only a 17/19 chance that the second uncontaminated bushel would be pulled. In short, we wrote: ( ) We notice that the numerator and denominator both have a product of two sequential numbers. Had they shipped, say, four bushels, the probability that all four were uncontaminated would be: As you might imagine, this pattern continues. How painful, though, would it be to have to multiply eight or nine probabilities of this nature together You could certainly do it, but you might think, “It sure would be nice to take advantage of this pattern!” Well, we‟re in luck! Let‟s define an important term: A factorial is a descending product of whole numbers down to 1, beginning at a specified whole number. To start with a generic whole number, , we denote this product by , and write: ( ) ( ) Example 1: Find . SOLUTION: By definition of factorial, we write Statistics for Decision-Making in Business © Milos Podmanik Page 119
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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
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 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: f. All numerical red cards are remo
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 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
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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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