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STA 210 Chapter 6 Homework –
actual solution
Connecting Relative Area to ProbabilityThe likelihood of college students playing corn hole is high, but have you ever thought about how likely it is that you will actually get the bag in the hole? If we take some liberties both with the game and with the specifics of the underlying probability, we can gain some understanding about the natural relationship between relative area and common-sense probability! The key will be to not overthink the problem. Question: Suppose you aren't very good at corn hole. In fact, suppose the best you can do is to know that your throw will at least hit
some random place on the board. If the surface of an official corn hole board looks like the diagram shown, what are the chances that it will hit the hole?Think of the bag as a very small item, and remember you don't really aim. Rather, your toss just lands at a random place on the board. Look at the picture on page 131. About 41 chance - ans-About 2.5 chances in 100, since 28.27/1152 = 0. Now suppose the corn hole board has a funny bell-shape, with the hole delineated by the two vertical line segments. Granted, this would be the height of nerd tailgating. Suppose also that the entire bell-shaped sheet is 8 square feet, just like a regulation corn hole board surface. We are still only
If you are just throwing the bean bag at the bell board at random, then how would you figure out the chances of the bag going into the hole in Board A? (graph on page 132) 8 divided by the area of the entire board The area of the board divided by the area of the hole The area of the hole in A divided by the area of the hole in B The area of the hole, divided by the area of the entire board - ans-The area of the hole, divided by the area of the entire board Face in Class BooksIn a 2012 Washington Post article entitled "Is College Too Easy? As Study Time Falls, Debate Rises," Daniel de Vise reports that "over the past half-century, the [average] amount of time college students
actually study — read, write, and otherwise prepare for class — has dwindled from 24 hours a week to about 15 ...." No standard deviation is given, but let's assume that standard deviation is 2.5 hours. Use this information to answer the next 3 questions. Question: Suppose a college student is selected at random. Use the empirical rule to estimate how likely it is that this student studies between 10 and 17.5 hours per week. about 13.5 chances in 100 About 50% of the time About 81.5 chances in 100 about 2.5 chances in 100 - ans-About 81. chances in 100
About 81.5 chances in 100 - ans-about 2. chances in 100 A 2012 study measured “the efficacy of social networking systems as instructional tools.†The study surveyed 186 students about the use of social networking systems as an active part of the semester class structure. One question asked and answered by 181 of the 186 students, along with the results received, is shown below.Question from the study: There are no specific benefits that make Facebook a better forum for class discussions and announcements than a learning management system like Blackboard. Do you agree or disagree?The mean of these 181 answers is 3.15, and the standard deviation is 1.05. Use this information for the next 2 questions.
Question: Use the empirical rule to estimate how likely it is that an answer to this question will be in the interval 2.10 to 4.20. What was the actual percentage of answers in this interval? Estimated is 81.5% and actual is 79.20% Estimated is 68% and actual is 61.33% Esti - ans-Estimated is 68% and actual is 61.33% Use the empirical rule to estimate how likely it is that an answer to this question will be above 4.20. What was the actual percentage of answers in this interval? Estimated is 81.5% and actual is 79.20% Estimated is 16% and actual is 9.9%
the center of the lane — even if only the smallest tip of one of Mo's hands is in the center of the lane. Question: How far to the left of the center line can Mo move the center of his body and still be able to deny the pass to the lane? HINT: use graph on page 134 12' 6' 18' +-3' - ans-6' Team data suggest that Mo will play within six feet on either side of the center line 68% of the time. He will play six-to-twelve feet to the left of the center line 13.5% of the time, and six-to-twelve feet to the right of the center line
13.5% of the time. Finally, he will only play in the lanes twelve-to-eighteen feet (left or right of center line) 2.35% of the time, respectively. (See diagram on page 135) Question: About what percentage of the time will Mo be in position to deflect a pass that is thrown dead center into the middle of the lane (right through the vertical red line)? Assume all passes thrown by the opposition will be at approximately chest level for Mo. About 68% of the time About 95% of the time About ±34% of the time About 81.5% of the time - ans-About 68% of the time
iv II III - ans-III Question: Please pick the best answer for Question 5b on page 135. iii i ii iv - ans-iv
