# Talk:QB/d Bell.binomial

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First to allow and display discussion of each question, and second, to store the quiz in raw-script for. ==[[QB/d_Bell.binomial]]== ===1=== *<!--CC0 [[user:Guy vandegrift]]-->The normal distribution (often called a "bell curve") is never skewed + True - False ====Discuss==== ===2=== *<!--CC0 [[user:Guy vandegrift]]-->The normal distribution (often called a "bell curve") is usually skewed - True + False ====Discuss==== This second (false) True-False question follows the policy that to prevent students from just memorizing that the "bell curve skew" question is either true or false. Such efforts to confuse students trying to memorize will become less necessary if [[Quizbank]] can be made very large, or if a private wiki can be arranged to host the instructor's "secret" questions. ===3=== *<!--CC0 [[user:Guy vandegrift]]-->By definition, a skewed distribution - is broader than an unskewed distribution - includes negative values of the observed variable - is a "normal" distribution + is asymmetric about it's peak value - contains no outliers ====Discuss==== This helps students recognize that the standard deviation rule applied to the binomial distribution is only approximate ===4=== *<!--CC0 [[user:Guy vandegrift]]-->The binomial distribution results from observing n outcomes, each having a probability p of "success" + True - False ====Discuss==== An easy question to help the student remember the definition of the binary distribution ===5=== *<!--CC0 [[user:Guy vandegrift]]-->What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as "two"? + 3/6 - 2/6 - 1/6 - 5/6 - 4/6 ====Discuss==== I deliberately randomized the order of the possible answers to alert students using [[Quizbank]] quizzes for the first time that answers to conceptual questions are not presented in any order (quizzes in [[:Category:QB/Numerical]] usually do have the answers in numerical order.) ===6=== *<!--CC0 [[user:Guy vandegrift]]-->What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as anything but "two"? - 3/6 - 2/6 - 1/6 + 5/6 - 4/6 ====Discuss==== Students need to know that "success" does not refer to good or bad, just a given outcome. ===7=== *<!--CC0 [[user:Guy vandegrift]]-->What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as either a "two" or a "three"? - 3/6 + 2/6 - 1/6 - 5/6 - 4/6 ====Discuss==== To clarify the meaning of "OR" ===8=== *<!--CC0 [[user:Guy vandegrift]]-->How would you describe the "skew" of a binary distribution? + The binary distribution is always skewed, but has little skew for a large number of trials n. - The binary distribution is always skewed, but has little skew for a small number of trials n. - The binary distribution is never skewed if it is a true binary distribution. - Distributions are never skewed. Only experimental measurements of them are skewed. - None of these are true. ====Discuss==== ===9=== *<!--CCO [[user:Guy vandegrift]]-->For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 90 trials are observed, then 68% of the time the observed number of positive outcomes will fall within ±___ of the expected value if p=.11 is the probability of a positive outcome. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution). - 6 - 18 + 3 - 9 - 1 ====Discuss==== σ where σ≈(90*.11*.9)<sup>1/2</sup>≈3 ===10=== *<!--CCO [[user:Guy vandegrift]]-->For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 40 trials are observed, then 68% of the time the observed number of positive outcomes will fall within ±___ of the expected value if p=.11 is the probability of a positive outcome. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution). - 6 - 18 - 3 - 9 + 2 ====Discuss==== σ where σ≈(40*.11*.9)<sup>1/2</sup>≈2 ===11=== *<!--CCO [[user:Guy vandegrift]]-->For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 40 trials are made and p=.11, the expected number of positive outcomes is__. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution. + 4.4 - 2.2 - 9.9 - 3.3 - 1.1 ====Discuss==== σ where σ≈(40*.11*.9)<sup>1/2</sup>≈2 ===12=== *<!--CCO [[user:Guy vandegrift]]-->For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 90 trials are made and p=.11, the expected number of positive outcomes is__. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution. - 2.2 + 9.9 - 3.3 - 1.1 ====Discuss==== σ where σ≈(40*.11*.9)<sup>1:2</sup>≈2 ===13=== *<!--CC0 [[user:Guy vandegrift]]-->Recall that only 4.6% of the outcomes for a normal distribution lie outside of two standard deviations from the mean, and approximate the binomial distribution as normal for large numbers. If the variance is σ<sup>2</sup>=np(1-p) where n is the number of trials and p=.11 is the probability of a positive outcome for 40 trials, roughly 98% of the outcomes will be smaller than approximately __ - 6 + 8 - 12 - 16 - 22 ====Discuss==== The mean is μ=np=4.4 and the standard deviation is σ=(40*1.1*.9)<sup>1/2</sup>=2. Two standard deviations above the mean is about 8.4 ===14=== *<!--CC0 [[user:Guy vandegrift]]-->Recall that only 4.6% of the outcomes for a normal distribution lie outside of two standard deviations from the mean, and approximate the binomial distribution as normal for large numbers. If the variance is σ<sup>2</sup>=np(1-p) where n is the number of trials and p=.11 is the probability of a positive outcome for 90 trials, roughly 98% of the outcomes will be smaller than approximately __ - 6 - 8 - 12 + 16 - 22 ====Discuss==== The mean is μ=np=9.9 and the standard deviation is σ=(90*1.1*.9)<sup>1/2</sup>=3. Two standard deviations above the mean is about 16 (note how this comment came after the question) ===15=== *<!--CC0 [[user:Guy vandegrift]]-->A local college averages 2500 new incoming students each year. Suppose the pool of potential high school graduates in the local area is so large that the probability of a given student selecting this college is small, and assume a variance of σ<sup>2</sup> equal to p(1-p). What standard deviation would you expect in the yearly total of new enrollees, assuming nothing changes in this population from year to year? + 50 - 150 + 500 - 200 - 250 ====Discuss==== ===16=== *<!--CC0 [[user:Guy vandegrift]]-->A local college averages 1600 new incoming students each year. Suppose the pool of potential high school graduates in the local area is so large that the probability of a given student selecting this college is small, and assume a variance of σ<sup>2</sup> equal to p(1-p). What standard deviation would you expect in the yearly total of new enrollees, assuming nothing changes in this population from year to year? + 16 - 160 + 40 - 10 - 32 ====Discuss==== ==Raw script== :t QB/d_Bell.binomial :! CC0 [[user:Guy vandegrift]] :? The normal distribution (often called a "bell curve") is never skewed :+ True :- False :! CC0 [[user:Guy vandegrift]] :? The normal distribution (often called a "bell curve") is usually skewed :- True :+ False :$ This second (false) True-False question follows the policy that to prevent students from just memorizing that the "bell curve skew" question is either true or false. Such efforts to confuse students trying to memorize will become less necessary if [[Quizbank]] can be made very large, or if a private wiki can be arranged to host the instructor's "secret" questions. :! CC0 [[user:Guy vandegrift]] :? By definition, a skewed distribution :- is broader than an unskewed distribution :- includes negative values of the observed variable :- is a "normal" distribution :+ is asymmetric about it's peak value :- contains no outliers :$ This helps students recognize that the standard deviation rule applied to the binomial distribution is only approximate :! CC0 [[user:Guy vandegrift]] :? The binomial distribution results from observing n outcomes, each having a probability p of "success" :+ True :- False :$ An easy question to help the student remember the definition of the binary distribution :! CC0 [[user:Guy vandegrift]] :? What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as "two"? :+ 3/6 :- 2/6 :- 1/6 :- 5/6 :- 4/6 :$ I deliberately randomized the order of the possible answers to alert students using [[Quizbank]] quizzes for the first time that answers to conceptual questions are not presented in any order (quizzes in [[:Category:QB/Numerical]] usually do have the answers in numerical order.) :! CC0 [[user:Guy vandegrift]] :? What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as anything but "two"? :- 3/6 :- 2/6 :- 1/6 :+ 5/6 :- 4/6 :$ Students need to know that "success" does not refer to good or bad, just a given outcome. :! CC0 [[user:Guy vandegrift]] :? What is the probability of success, p, for a binary distribution using a six-sided die, with success defined as either a "two" or a "three"? :- 3/6 :+ 2/6 :- 1/6 :- 5/6 :- 4/6 :$ To clarify the meaning of "OR" :! CC0 [[user:Guy vandegrift]] :? How would you describe the "skew" of a binary distribution? :+ The binary distribution is always skewed, but has little skew for a large number of trials n. :- The binary distribution is always skewed, but has little skew for a small number of trials n. :- The binary distribution is never skewed if it is a true binary distribution. :- Distributions are never skewed. Only experimental measurements of them are skewed. :- None of these are true. :! CCO [[user:Guy vandegrift]] :? For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 90 trials are observed, then 68% of the time the observed number of positive outcomes will fall within ±___ of the expected value if p=.11 is the probability of a positive outcome. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution). :- 6 :- 18 :+ 3 :- 9 :- 1 :$ σ where σ≈(90*.11*.9)<sup>1/2</sup>≈3 :! CCO [[user:Guy vandegrift]] :? For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 40 trials are observed, then 68% of the time the observed number of positive outcomes will fall within ±___ of the expected value if p=.11 is the probability of a positive outcome. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution). :- 6 :- 18 :- 3 :- 9 :+ 2 :$ σ where σ≈(40*.11*.9)<sup>1/2</sup>≈2 :! CCO [[user:Guy vandegrift]] :? For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 40 trials are made and p=.11, the expected number of positive outcomes is__. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution. :+ 4.4 :- 2.2 :- 9.9 :- 3.3 :- 1.1 :$ σ where σ≈(40*.11*.9)<sup>1/2</sup>≈2 :! CCO [[user:Guy vandegrift]] :?For a binomial distribution with n trials, the variance is σ<sup>2</sup>=np(1-p). If 90 trials are made and p=.11, the expected number of positive outcomes is__. Make the approximation that this binomial distribution is approximately a Gaussian (normal) distribution. : - 4.4 :- 2.2 :+ 9.9 :- 3.3 :- 1.1 :$ σ where σ≈(40*.11*.9)<sup>1:2</sup>≈2 :! CC0 [[user:Guy vandegrift]] :? Recall that only 4.6% of the outcomes for a normal distribution lie outside of two standard deviations from the mean, and approximate the binomial distribution as normal for large numbers. If the variance is σ<sup>2</sup>=np(1-p) where n is the number of trials and p=.11 is the probability of a positive outcome for 40 trials, roughly 98% of the outcomes will be smaller than approximately __ :-6 :+8 :-12 :-16 :-22 :$ The mean is μ=np=4.4 and the standard deviation is σ=(40*1.1*.9)<sup>1/2</sup>=2. Two standard deviations above the mean is about 8.4 :! CC0 [[user:Guy vandegrift]] :? Recall that only 4.6% of the outcomes for a normal distribution lie outside of two standard deviations from the mean, and approximate the binomial distribution as normal for large numbers. If the variance is σ<sup>2</sup>=np(1-p) where n is the number of trials and p=.11 is the probability of a positive outcome for 90 trials, roughly 98% of the outcomes will be smaller than approximately __ :-6 :-8 :-12 :+16 :-22 :$ The mean is μ=np=9.9 and the standard deviation is σ=(90*1.1*.9)<sup>1/2</sup>=3. Two standard deviations above the mean is about 16 (note how this comment came after the question) :! CC0 [[user:Guy vandegrift]] :? A local college averages 2500 new incoming students each year. Suppose the pool of potential high school graduates in the local area is so large that the probability of a given student selecting this college is small, and assume a variance of σ<sup>2</sup> equal to p(1-p). What standard deviation would you expect in the yearly total of new enrollees, assuming nothing changes in this population from year to year? :+50 :-150 :+500 :-200 :-250 :$ :! CC0 [[user:Guy vandegrift]] :? A local college averages 1600 new incoming students each year. Suppose the pool of potential high school graduates in the local area is so large that the probability of a given student selecting this college is small, and assume a variance of σ<sup>2</sup> equal to p(1-p). What standard deviation would you expect in the yearly total of new enrollees, assuming nothing changes in this population from year to year? :+16 :-160 :+40 :-10 :-32 :$ :z