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Chapter 5: Q 3 (page 220)
Are the values found in Exercise 2 statistics or parameters? Why?
The values are parameters.
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Ultimate Binomial Exercises! Exercises 37鈥�40 involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities.
M&Ms Data Set 27 鈥淢&M Weights鈥� in Appendix B includes data from 100 M&M candies, and 19 of them are green. Mars, Inc. claims that 16% of its plain M&M candies are green. For the following, assume that the claim of 16% is true, and assume that a sample consists of 100 M&Ms.
a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 19 green M&Ms significantly high?
b. Find the probability of exactly 19 green M&Ms.
c. Find the probability of 19 or more green M&Ms.
d. Which probability is relevant for determining whether the result of 19 green M&Ms is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 19 green M&Ms significantly high?
e. What do the results suggest about the 16% claim by Mars, Inc.?
In Exercises 21鈥�24, assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey).
If 20 adult smartphone users are randomly selected, find the probability that exactly 15 of them use their smartphones in meetings or classes.
In Exercises 1鈥�5, assume that 74% of randomly selected adults have a credit card (based on results from an AARP Bulletin survey). Assume that a group of five adults is randomly selected.
If all five of the adults have credit cards, is five significantly high? Why or
why not?
Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.
News Source Based on data from a Harris Interactive survey, 40% of adults say that they prefer to get their news online. Four adults are randomly selected.
a. Use the multiplication rule to find the probability that the first three prefer to get their news online and the fourth prefers a different source. That is, find P(OOOD), where O denotes a preference for online news and D denotes a preference for a news source different from online.
b. Beginning with OOOD, make a complete list of the different possible arrangements of those four letters, then find the probability for each entry in the list.
c. Based on the preceding results, what is the probability of getting exactly three adults who prefer to get their news online and one adult who prefers a different news source.
Identifying Binomial Distributions. In Exercises 5鈥�12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.
Investigating Dates In a survey sponsored by TGI Friday鈥檚, 1000 different adult respondents were randomly selected without replacement, and each was asked if they investigate dates on social media before meeting them. Responses consist of 鈥測es鈥� or 鈥渘o.鈥�
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