242 CHAPTER 5 Discrete Probability Distributions Rates,” by Lawrence, Hong, and Cherrier). Also assume that Delta Airlines accepts 200 reservations for the 180 seats that are available. • Find the probability that when 200 reservations are accepted for Delta Airlines Flight 2673, there are more passengers showing up than there are seats available. Is the probability of overbooking small enough so that it does not happen very often, or does it seem too high so that changes must be made to make it lower? • Use trial and error to find the maximum number of reservations that could be accepted so that the probability of having more passengers than seats is 0.05 or less. FROM DATA TO DECISION Critical Thinking: Using probability to test a claim Consider a Kaspersky Lab survey of 2515 adult Internet users in the United States and Canada. Among those 2515 survey subjects, 46% said that they experienced at least one cybersecurity issue within the past five years. The cybersecurity issues include problems such as viruses, ransomware attacks, or malicious email. Here is a key question about this survey: Do the survey data support a claim that fewer than half (or fewer than 50%) of adult Internet users have experienced cybersecurity issues within the past five years? Clearly, 46% is less than 50%, but is 46% significantly less than 50%? Use the methods of this chapter to determine whether 46% is significantly less than 50% in this case. Address these questions: a. Among the 2515 survey subjects, what is the actual number of them who said that they experienced at least one cybersecurity issue within the past five years? b. Given the context of the Kaspersky Lab survey, is 46% significantly less than 50% in this case? Explain using relevant probabilities. c. Based on the results from part (b), what should be concluded about the claim that fewer than half (or fewer than 50%) of adult Internet users have experienced cybersecurity issues within the past five years? d. For this survey, would a result of 49.9% be significantly less than 50%? e. For this survey, would a result of 10% be significantly less than 50%? 1.In-class activity Win $1,000,000! The James Randi Educational Foundation offered a $1,000,000 prize to anyone who can show “under proper observing conditions, evidence of any paranormal, supernatural, or occult power or event.” (That prize was discontinued in 2015.) Divide into groups of three. Select one person who will be tested for extrasensory perception (ESP) by trying to correctly identify a digit (0–9) randomly selected by another member of the Cooperative Group Activities Refer to Data Set 45 “Births in New York” from Appendix B. a. Find the number of male births and find the number of female births. (Manual counting of those numbers is totally impractical given the sample size of n = 465,506.) Assuming that 0.512 of births are males (as is commonly believed), find the probability of getting a number of male births that is at least as extreme as the number of male births in the data set. What does the result suggest about the common belief that 0.512 of births are male births? b. Construct a frequency distribution with the values of x consisting of the different lengths of stay paired with their corresponding frequencies. How many different values are there for lengths of stay? c. Investigate whether the lengths of stay have a distribution that is approximately a Poisson distribution. Explain the approach used and state a conclusion. Big (or Very Large) Data Project
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