STA 210 Chapter 6 Homework

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% Estimated is 68% and actual is 61.33% Estimated is 95% and actual is 94.28%

Estimated is 16% and actual is 9.9%

Question: Please pick the best answer for Question 5b on page 135. iii i ii iv

iv

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

About 68% of the time

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

About 81.5 chances in 100

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

The area of the hole, divided by the area of the entire board

Off the court, Mo has his own problems trying to pass statistics class. In particular, he is trying to understand confidence intervals for proportions a little better. The sampling distribution of the sample proportion is shown again here. Think of the horizontal axis in the figure as where the sample proportion p̂ moves about from sample to sample, much the way Mo's feet do on defense. The diagram just tells us the chance of pˆ being in certain places along the x-axis. The very center of the diagram is where the unknown parameter p resides. Refer to the diagram on page 135 at the bottom. Question: Please pick the best answer for Question 5a on page 135. I iv II III

III

Coach Linguini is trying to develop the defense of his new center Mo Biggs. Mo is an amazing talent with a truly unbelievable 12-foot wingspan (distance from tip of left fingers to tip of right fingers with arms outstretched). Mo's team is playing an opponent known to pass right into the middle of the lane. (See vertical red dotted line in graphic.) Coach wants Mo to play defense by shuffling his feet along the blue dotted line tangent to the free throw circle. Coach knows that, depending on what the opposing offense is doing, Mo might have to move to the left or the right, but he feels Mo can deny a pass into 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'

6'

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 chances in 100 since 1152/28.27 is 40.75 About 4.1 chances in 100 since 1152/28.27 is 40.75 About 2.5 chances in 10 since 28.27/1152 = 0.0245 About 2.5 chances in 100, since 28.27/1152 = 0.0245

About 2.5 chances in 100, since 28.27/1152 = 0.0245

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 guaranteed that our throw will land someplace randomly on the board. Look at the graphs on page 132. Question: Suppose you toss the bean bag at random toward the board, just as in a. Which of the two bell boards, A or B, would be better to play on and why? Board B since there is a smaller chance of the bag going in the hole Board B since there is a greater chance of the bag going in the hole Board A since there is a smaller chance of the bag going in the hole Board A since there is a greater chance of the bag going in the hole

Board A since there is a greater chance of the bag going in the hole

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% Estimated is 16% and actual is 9.9% Estimated is 95% and actual is 94.28%

Estimated is 68% and actual is 61.33%

Suppose a college student is selected at random. Use the empirical rule to estimate how likely it is that this student studies between 17.5 and 20 hours per week. about 81.5 chances in 100 about 50% of the time about 2.5 chances in 100 about 13.5 chances in 100

about 13.5 chances in 100

Suppose a college student is selected at random. Use the empirical rule to estimate how likely it is that this student studies more than 20 hours per week. about 13.5 chances in 100 about 50% of the time about 2.5 chances in 100 About 81.5 chances in 100

about 2.5 chances in 100