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Chapter 5: Q. 6 (page 309)

Keep on tossing The figure shows the results of two different sets of5000coin tosses.

Explain what this graph tells you about chance behavior in the short run and the long run.

Short Answer

Expert verified

In the short run, values will be different than the proportion of .5while in the long run, the probability of heads will be about0.5.

Step by step solution

01

Given information

We have been given the results of two different sets of 5000coin tosses.

We need to find out the chance behavior in the short run and the long run from the graph.

02

Explanation

In the short run due to different peaks present below and above the proportion of 0.5there is a variation in the result very much and due to this, it takes on values very different than a proportion of 0.5.

In the long run, the proportion always tends to be about 0.5and this implies that the long-run frequency is about 0.5so the probability of heads will be about0.5.

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Most popular questions from this chapter

Which of the following is a correct way to perform the simulation?

a. Let integers from 1to34represent making a free throw and 35to50represent missing a free throw. Generate 50random integers from1to50. Count the number

of made free throws. Repeat this process many times.

b. Let integers from 1to34represent making a free throw and 35to50represent missing a free throw. Generate 50 random integers from 1 to 50 with no repeats

allowed. Count the number of made free throws. Repeat this process many times.

c. Let integers from1to56represent making a free throw and 57to100represent missing a free throw. Generate 50 random integers from1to100.Count the number of made free throws. Repeat this process many times.

d. Let integers from localid="1653986588937" 1to56represent making a free throw and localid="1653986593808" 57to100represent missing a free throw. Generate 50 random integers from localid="1653986598680" 1to100with no repeats allowed. Count the number of made free throws. Repeat this process many times.

e. None of the above is correct.

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Random assignment Researchers recruited 20volunteers-8men and 12women-to take part in an experiment. They randomly assigned the subjects into two groups of 10people each. To their surprise, 6of the 8men were randomly assigned to the same treatment. Should they be surprised? We want to design a simulation to estimate the probability that a proper random assignment would result in 6or more of the 8men ending up in the same group.

Get 20identical slips of paper. Write "M" on 8of the slips and "W" on the remaining 12slips. Put the slips into a hat and mix well. Draw 10of the slips without looking and place into one pile representing Group 1. Place the other 10slips in a pile representing Group 2. Record the largest number of men in either of the two groups from this simulated random assignment. Repeat this process many, many times. Find the percent of trials in which 6or more men ended up in the same group.

Dogs and cats In one large city, 40%of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household. What鈥檚 the probability that the household owns a dog or a cat?
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