5.66 Attitudes toward drinking and studies of behavior. Some of the methods in this section are approximations rather than exact probability results. We have given rules of thumb for safe use of these approximations. (a) You are interested in attitudes toward drinking among the 75 members of a fraternity. You choose 30 members at random to interview. One question is "Have you had five or more drinks at one time during the last week?" Suppose that, in fact, 30% of the 75 members would say Yes. Explain why you cannot safely use the B(30, 0.3) distribution for the count X in your sample who say Yes. (b) The National AIDS Behavioral Surveys found that 0.2% (that's 0.002 as a decimal fraction) of adult heterosexuals had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS. Suppose that this national proportion holds for your region. Explain why you cannot safely use the Normal approximation for the sample proportion who fall in this group when you interview an SRS of 1000 adults.

This problem involves empirical probability. The table shows the breakdown of 86 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is in the Army. Male Female Total Army 25 10 35 Navy 23 7 30 Marine Corps 6 1 7 Air Force 10 4 14 Total 64 22 86 The probability that a randomly selected single parent in the U.S. military is in the Army is (Type an integer or decimal rounded to the nearest hundredth as needed.)

Dinner at Home. Choose a parent with children under age 18 in the United States at random and ask, "How many nights a week out of seven does your family eat dinner together at home?" Call the response X for short. Based on a large sample survey, here is a probability model for the answer you will get:0 Nights 1 3 4 6. 7 Probability 0.05 0.00 0.07 0.08 0.10 0.17 0.15 0.38 (a) Verify that this is a valid finite probability model. (b) Describe the event X<4 in words. What is P(X<4)? (c) Express the event "eat dinner together at home at least once a week" in terms of X. What is the probability of this event?

According to the recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy. Assume 150 patients decide to get their genome sequenced. If the claim by scientists is accurate, what is the probability that fewer than 70% of the patientswill get a correct diagnosis for extreme longevity? Group of answer choices A. 0.1422 B. 0.0722 C. 0.2214 D. 0.0208

This problem involves empirical probability. The table shows the breakdown of 98 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force. Marine Air Force Corps 8 12 5 17 Male Female Total Army 25 10 35 Navy 28 8 36 2 10 Total 73 25 98 The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is (Type an integer or decimal rounded to the nearest hundredth as needed.)

This problem involves empirical probability. The table shows the breakdown of 85 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force. Marine Air Corps Force 5 13 1 5 6 18 Male Female Total Army 23 9 32 Navy 22 7 29 Total 63 22 85 The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is (Type an integer or decimal rounded to the nearest hundredth as needed.)

Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. Undergraduate Major Intended Enrollment Status Full-Time Part-Time Intended Enrollment Status Full-Time Part-Time Totals 514 a. Develop a joint probability table for these data (to 4 decimals). Totals Business 344 170 Engineering 200 Business 169 I 369 Undergraduate Major Engineering Other Other Totals 238 782 196 434 535 1,317 Totals b. Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA students. Select your answer - + c. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major (to 4 decimals)? d. If a student was an undergraduate business major, what is the probability…