soln%206 - X X X X X X X X X X X X X X X X X AP Statistics...

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X X X X X X X X X X X X X X X X X AP Statistics Solutions to Packet 6 X Probability The Study of Randomness The Idea of Probability Probability Models General Probability Rules X X X X X X X X X X X X X
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2 HW #37 3, 4, 8, 11, 14, 15, 17, 18 6.3 SHAQ The basketball player Shaquille O’Neal makes about half of his free throws over an entire season. We will use the calculator to simulate 100 free throws shot independently by a player who has probability 0.5 of making each shot. We let the number 1 represent the outcome “Hit” and 0 represent a “Miss.” (a) Enter the command randInt(0, 1, 100) SHAQ. This tells the calculator to randomly select a hit (1) or a miss (0), do this 100 times in succession, and store the results in the list named SHAQ. (b) What percent of the 100 shots are hits? In our simulation, Shaq hit 52% of his shots. (c) Examine the sequence of hits and misses. How long was the longest run of shots made? Of shots missed? (Sequences of random outcomes often show runs longer than our intuition thinks likely.) The longest sequence of misses in our run was 6 and the longest sequence of hits was 9. Of course, results will vary. 6.4 MATCHING PROBABILITIES Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement about an event. (The probability is usually a much more exact measure of likelihood than is the verbal statement.) 0, 0.01, 0.3, 0.6, 0.99, 1 (a) This event is impossible. It can never occur. 0 (b) This event is certain. It will occur on every trial of the random phenomenon. (c) This event is very unlikely, but it will occur once in a while in a long sequence of trials. 0.01 (d) This event will occur more often than not. 0.6 6.8 THREE OF A KIND You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. Explain in simple language what this means. In the long run, of a large number of hands of five cards, about 2% (one out of 50) will contain a three of a kind. (Note: This probability is actually 88 4165 = 0.02113.)
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3 6.11 DESCRIBE THE SAMPLE SPACE In each of the following situations, describe a sample space S for the random phenomenon. In some cases you have some freedom in specifying S, especially in setting the largest and the smallest value in S. (a) A seed is planted in the ground. It either germinates or fails to grow. S = {germinates, fails to grow}. (b) A patient with a usually fatal form of cancer is given a new treatment. The response variable is the length of time that the patient lives after treatment. If measured in weeks, for example, S = {0, 1, 2, . . .}. (c) A student enrolls in a statistics course and at the end of the semester receives a letter grade. S = {A, B, C, D, F}. (d) A basketball player shoots four free throws. You record the sequence of hits and misses. Using Y for “yes (shot made)” and N for “no (shot missed),” S = {YYYY, NNNN, YYYN, NNNY, YYNY, NNYN, YNYY, NYNN, NYYY, YNNN, YYNN, NNYY, YNYN, NYNY, YNNY, NYYN}. (There are 16 items in the sample space.) (e) A basketball player shoots four free throws. You record the number of baskets she makes.
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soln%206 - X X X X X X X X X X X X X X X X X AP Statistics...

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