Statistics: Informed Decisions Using Data 5th Edition solutions

Statistics: Informed Decisions Using Data 5
Double Jackpot Shawn lives near the border of Illinois and Missouri. One weekend he decides to play $1 in both state lotteries in hopes of hitting two jackpots. The probability of winning the Missouri Lotto is about 0.00000028357 and the probability of winning the Illinois Lotto is about 0.0000000982

Statistics: Informed Decisions Using Data 5
False Positives The ELISA is a test to determine whether the HIV antibody is present. The test is 99.5% effective, which means that the test will come back negative if the HIV antibody is not present 99.5% of the time. The probability of a test coming back positive when the antibody is not present (a

Statistics: Informed Decisions Using Data 5
Christmas Lights Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or failure of a bulb is independent

Statistics: Informed Decisions Using Data 5
Life Expectancy The probability that a randomly selected 40-year-old male will live to be 41 years old is 0.99757, according to the National Vital Statistics Report, Vol. 56, No. 9. (a) What is the probability that two randomly selected 40-year old males will live to be 41 years old? (b) What i

Statistics: Informed Decisions Using Data 5
Life Expectancy The probability that a randomly selected 40-year-old female will live to be 41 years old is 0.99855 according to the National Vital Statistics Report, Vol. 56, No. 9. (a) What is the probability that two randomly selected 40-year old females will live to be 41 years old? (b) Wha

Statistics: Informed Decisions Using Data 5
Derivatives In finance, a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage has a probability of 0.01 of default. (a) What is the probability a randomly selected mortgage will not default (tha

Statistics: Informed Decisions Using Data 5
Quality Control Suppose that a company selects two people who work independently inspecting two-by-four timbers. Their job is to identify low-quality timbers. Suppose that the probability that an inspector does not identify low-quality timber is 0.20. (a) What is the probability that both inspector

Statistics: Informed Decisions Using Data 5
Reliability and Redundancy In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial compone

Statistics: Informed Decisions Using Data 5
Reliability For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure. (a) Would it be unusual to observe one component fail?

Statistics: Informed Decisions Using Data 5
Reliability and Redundancy, Part II See Problem 21. Suppose a particular airline component has a probability of failure of 0.03 and is part of a triple modular redundancy system. (a) What is the probability the system does not fail? (b) Engineers decide the probability of failure is too high fo

Statistics: Informed Decisions Using Data 5
Cold Streaks Players in sports are said to have hot streaks and cold streaks. For example, a batter in baseball might be considered to be in a slump, or cold streak, if he has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 30% of the time he comes to the plate

Statistics: Informed Decisions Using Data 5
Bowling Suppose that Ralph gets a strike when bowling 30% of the time. (a) What is the probability that Ralph gets two strikes in a row? (b) What is the probability that Ralph gets a turkey (three strikes in a row)? (c) When events are independent, their complements are independent as well.

Statistics: Informed Decisions Using Data 5
Driving under the Influence Among 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds are selected at random. Source: U.S. Department of Health and Human Services, reported in USA Today (a) What is the probability that all three

Statistics: Informed Decisions Using Data 5
Defense System Suppose that a satellite defense system is established in which four satellites acting independently have a 0.9 probability of detecting an incoming ballistic missile. What is the probability that at least one of the four satellites detects an incoming ballistic missile? Would you feel

Statistics: Informed Decisions Using Data 5
Audits and Pet Ownership According to Internal Revenue Service records, 6.42% of all household tax returns are audited. According to the Humane Society, 39% of all households own a dog. Assuming dog ownership and audits are independent events, what is the probability a randomly selected household is

Statistics: Informed Decisions Using Data 5
Weight Gain and Gender According to the National Vital Statistics Report, 20.1% of all pregnancies result in weight gain in excess of 40 pounds (for singleton births). In addition, 49.5% of all pregnancies result in the birth of a baby girl. Assuming gender and weight gain are independent, what is th

Statistics: Informed Decisions Using Data 5
Stocks Suppose your financial advisor recommends three stocks to you. He claims the likelihood that the first stock will increase in value at least 10% within the next year is 0.7, the likelihood the second stock will increase in value at least 10% within the next year is 0.55, and the likelihood the

Statistics: Informed Decisions Using Data 5
Betting on Sports According to a Gallup Poll, about 17% of adult Americans bet on professional sports. Census data indicate that 48.4% of the adult population in the United States is male. (a) Assuming that betting is independent of gender, compute the probability that an American adult selected at

Statistics: Informed Decisions Using Data 5
Fingerprints Fingerprints are now widely accepted as a form of identification. In fact, many computers today use fingerprint identification to link the owner to the computer. In 1892, Sir Francis Galton explored the use of fingerprints to uniquely identify an individual. A fingerprint consists of rid

Statistics: Informed Decisions Using Data 5
You Explain It! Independence Suppose a mother already has three girls from three separate pregnancies. Does the fact that the mother already has three girls affect the likelihood of having a fourth girl? Explain.

Statistics: Informed Decisions Using Data 5
You Explain It! Independence Ken and Dorothy like to fly to Colorado for ski vacations. Sometimes, however, they are late for their flight. On the air carrier they prefer to fly, the probability that luggage gets lost is 0.012 for luggage checked at least one hour prior to departure. However, the pro

Statistics: Informed Decisions Using Data 5
Two events E and F are _____ if the occurrence of event E in a probability experiment does not affect the probability of event F.

Statistics: Informed Decisions Using Data 5
The word and in probability implies that we use the _____ Rule.

Statistics: Informed Decisions Using Data 5
The word or in probability implies that we use the _____ Rule.

Statistics: Informed Decisions Using Data 5
True or False: When two events are disjoint, they are also independent.

Statistics: Informed Decisions Using Data 5
If two events E and F are independent, P(E and F) = _____ .

Statistics: Informed Decisions Using Data 5
Suppose events E and F are disjoint. What is P(E and F)?

Statistics: Informed Decisions Using Data 5
Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: Speeding on the interstate. F: Being pulled over by a police officer. (b) E: You gain weight. F: You eat fast food for dinner every night. (c) E: You get a high score on a statistics exam. F: The

Statistics: Informed Decisions Using Data 5
Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: The battery in your cell phone is dead. F: The batteries in your calculator are dead. (b) E: Your favorite color is blue. F: Your friends favorite hobby is fishing. (c) E: You are late for school.

Statistics: Informed Decisions Using Data 5
Suppose that events E and F are independent, P(E) = 0.3 and P(F) = 0.6. What is the P(E and F)?

Statistics: Informed Decisions Using Data 5
Suppose that events E and F are independent, P(E) = 0.7 and P(F) = 0.9. What is the P(E and F)?

Statistics: Informed Decisions Using Data 5
Flipping a Coin What is the probability of obtaining five heads in a row when flipping a fair coin? Interpret this probability.

Statistics: Informed Decisions Using Data 5
Rolling a Die What is the probability of obtaining 4 ones in a row when rolling a fair, six-sided die? Interpret this probability.

Statistics: Informed Decisions Using Data 5
Southpaws About 13% of the population is left-handed. If two people are randomly selected, what is the probability that both are left-handed? What is the probability that at least one is right-handed?