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Revision of Preparing For The AP Statistics Exam Chapter 5 Some more changes to earlier chapters: Ch Sec Pg Prob Change 2 2 15 MC4 Drop answer (E) Answer Change Add to stem: If all of theses choices can be generated, then select answer (E). 2 5 30 MC9 Drop answer (E) Add to stem: If (A) through (D) are true, then select answer (E). 3. 3 46 MC1 Drop answer (E) Add to stem: If each statement is a correct interpretation of r = -0.30, then select answer (E). 3 3 46 MC3 Drop answer (E) Add to stem: If each statement is true about a correlation coefficient, then select answer (E). 3 4 52 MC2 Drop answer (E) Add to stem: If all of (A) through (D) are reasonable conclusions, then select answer (E). 3 6 65 MC2 Drop answer (E) Add to stem: If all of (A) through (D) are reasonable techniques, then select answer (E). 3 Ch 70 MC2 Assess Drop answer (E) Add to stem: If all of (A) through (D) true, then select answer (E). 3 Ch 70 Assess MC6 Change answer (E) Two different sets of data can have the same set of z-scores. Still seems a little weird to me to drop E from the list of options… Chapter 5 Sec Pg 98 Prob Change Very end of page, could delete “percent” option or discuss it separately (especially since next line talks about being between 0 and 1)? 99 Around example 2 I noticed that the book isn’t too Answer Change consistent on P(A) vs. P(A) (italicizing of ()s). Not a big deal. 2nd result of basic probability rules, probably better to talk 100 about the events being complements rather than the probabilities? 100 Ex 4 Really want a sample proportion that is that far from .5? Could also use symbols in here? 1 How about “is greater than some fixed number a.”? 101 Para 1 102 MC3 Change answer (E) to S < 12. This is MC2? 103 MC4 The font in choice I is different. For choice II, how about “it has been determined that the probability is .12 that an inhabitant…” 103 MC5 Could include YXXZ as a distractor? I couldn’t justify any others but (A)? 103 FR3b Answer is wrong? Should be neither? (see later calculation of probability) Also, could say “if repeatedly roll pairs of dice”. I was also a little confused in (d). Can’t success – “accident in 50 miles” (you have fixed the distance), could say the probability depends on which 50 mile stretch type thing? 104 Ex 1 Maybe in b. some thing like “the probability of obtaining an ace of the 2nd draw is again 4/52, regardless of the outcome of the first draw? 105 Cond Before the last formula, do you mean to refer to the prob calculation of condition probability rather than the Multiplication rule? 2 108 MC2 Drop both questions. See replacements below. MC3 2 108 MC6 Change answer (E) to 0.97 110 Ex 2 Maybe say “How many ways can you select and arrange 4 out of 7…” 110 Tech Is MATH PRB true across different brands? Later you note refer to TI 83, need to here? Are you purposely not using P(S=3) type notation here? Do you want to justify why the multiplier in the binomial is a combination rather than a permutation more? 3 117 TEXT Last line in Example 5 should read (30/36)(30/36)(6/36)=25/216 4 118 MC4 Drop answer (E) Add to stem: If all are shared by binomial and geometric probability situations, then select answer (E). 118 Mc5 Want to add strictly to A? 119 FR5 Seems out of place when you told them to assume it was true in 3-8 119 FR8 Reword this one? For example: A teacher constructs his exams so that 70% of the time all students will pass the exam… (I got lost of the all of students vs. of the time) 5 119 Intro Change “treat” to “consider” in first paragraph? I wonder if these should not be called “probability plots” since that has a different technical meaning. Maybe probability function? Some books call them probability histograms… 120 Tech I don’t have a calculator here is “seq(x,x,0,4,1)” correct? It note confused me I’m also torn on calling this “standard error” instead of 121 standard deviation 122 Ex 3 Want to calculate the standard deviation for them? 122 MC2- Should it say “of the legitimate distributions”? Could 3 change explanation in 3 from “smallest range” to “probabilities are concentrated in a smaller range of values”? 5 122 MC4 Should stem say something about “all” distributions? Change answer (E); The graph of the distribution is skewed left. MC 6 A little awkward to go back and forth between probability distributions and data in this way 6 124 OE 1 Same question about “probability plots” OE 5 Change “determine” to ‘decide”? Para 1 After cdf how about “and therefore the probability, under the curve from negative infinity to the value of interest of the continuous random variable? 125 Ex 1 Want to tell them to label the variable on the horizontal axis and do so in the solution? 126 Calc 1. How about The first two parameters must be included. The last two are optional and if not included the calculator will use…” Also, is the TI really “representing infinity” or are we just using a very large and a very small number in its place? 127 Ex 4 At very end of box say something “is close to .80”? 128 MC1 Why is D wrong and could say “which is a true statement about the 80th percentile” unless D is wrong because it is not a definition? 6 128 MC3 Answer on page 344: add the underlined words, please: Using z-scores to calculate percentages of data should… Could talk about probabilities instead of percentages of data? 129 Para 2 How about “we are finding a discrete probability using a continuous distribution.” 132-3 The approximation comparisons are a little strange, some of the ones you say aren’t so good have a smaller absolute difference that the ones you say are good? 133 Notes Delete 1 or reword at least about the sum of the y coordinates? *Do you ever want to mention anywhere that P(X=x) must be zero for a continuous rv? Also could reinforce that with continuous P(X 133 MC1 x) = P(X<x)? Reword (D): the binomial distribution is not so severely skewed that..” 136 Ex 4 Isn’t this a good example of the difference between 3X and X1+X2+X3? I would change SD calculation and really reinforce that here. 7 138 MC1 133? 7 138 Change answer 1: Sample size must be large enough to reduce non-response bias in the data. MC2 Change stem to correct. MC2 In stem, reword as “A new game with two dice is being 133? 138 played on some…”? 8 139 FR3 Change beginning of problem: The American Mathematics Exam (AMC-12)…. has 150 possible points while the American Invitational Exam (AIME) has only 15 possible points. In order to invited to take the AIME, a students must score at least 100 on the AMC-12 exam….. 9 139 Intro Are 1. and 2. for discrete or for both? If both, maybe say the probability of the sample space needs to be one? The term probability density function is being used with discrete variables. Let’s not use “density” here. Could use “mass” as in other locations… 140 Ex The domain of B(10,.3) 141 Pre Want to say “or N(, )” here? Ex4 142 Chi 142 Want to label the two curves? Bottom 2 paragraphs seem a little mis-ordered. Could insert last paragraph before “If this parameter is deleted…” 9 143 MC2 Drop answer (E) Add to stem: If all of (A) through (D) define legitimate uniform probability density functions, then select answer (E). 143 MC4 Maybe more symmetric instead of (or in addition to) flatter? 144 Ex 1 I got a little confused in sum(randInt) explanation. Maybe something like “Therefore, the statement sum(randInt(0,9,10) 3) totals the number of 1’s in the list of Boolean outcomes”? 145 Before b I would just say “So the mean of these trials, 96/23=4.1739, estimates the expected number of boxes we would have to buy until a picture of Babe Ruth appears.” (I don’t like the “a minimum of 5 boxes…” 145 OE1 Really want same probability as in the preceding example? 146 4 In stem, was 15% supposed to be changed to 20% or change solution? d. to estimate the expected number of events that will occur 148 FR5 Don’t use density in the first sentence, maybe “Probability functions generate… between the density functions for continuous variables and mass functions for discrete variables.” 341 MC5 Could change “percent” to “proportion” 342 MC7 Change .06 to .006 347 9 347 IT2 Were some “not”s still supposed to be deleted? Did graph still need to be changed? Replacement for MC2 and MC3 in section 5.2, page 108. Use the following to answer questions 2 and 3. The results of a survey of 50 high school students’ choice of favorite pet is summarized in the table below: Dog Cat Other Girls 15 10 5 Boys 12 3 5 What is the probability that one of the survey students, selected at random will be 2. A girl whose favorite pet is a cat? (A) 10/50 (B) 10/13 (C) 10/30 (D) 13/50 (E) 30/50 (D) 13/50 (E) 30/50 3. A girl given that cat was the selected favorite pet? (A) 10/50 answers A and B? (B) 10/13 (C) 10/30