The table to the right gives a breakdown of 2,149 civil cases that were appealed. The outcome of the appeal, as well as the type of trial (judge or jury), was determined for each case. Suppose one of the cases is selected at random and the outcome of the appeal and type of trial are observed.
Zoologists investigated the likelihood of fallow deer bucks during the mating season. Researchers recorded 163 encounters between two bucks, one of which clearly initiated the encounter with the other. In these 163 initiated encounters, the zoologists kept track or not a physical contact fight occurred and whether the initiator ultimately won or lost the encounter. Suppose we select one of these 163 encounters and note the outcome (fight status and winner). Complete parts a through c.
Suppose 90% of kids who visit a doctor have a fever, and 10% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?
A table of classifying a sample of 78 patrons of a restaurant according to type of meal and their rating of the service is shown to the right. Suppose we select, at random, one of the 78 patrons. Given that the meal was dinner, what is the probability that the service was good?
The chance of winning a lottery game is 1 in approximately 26 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $4 million grand prize. Calculate your expected net winnings for this single ticket. Interpret the result.
In a driver-side “star” scoring system for crash-testing new cars, each crash-tested car is given a rating from one star to five stars; the more stars in the rating the better is the level of crash protection in a head-on collision. A summary of the driver-side star ratings for 98 cars is reproduced in the accompanying table. Assume that 1 of 98 cars is selected at random, and let x equal the number of stars in the car’s driver-side star rating. Complete parts a through d.
If x is a binomial random variable, use the binomial probability table to find the probabilities below.
If x is a binomial random variable, calculate µ, σ^2, and σ for each of the following values of n and p. Complete parts a through f.
A country’s government has devoted considerable funding to missile defense research over the past 20 years. The latest development is the Space-Based Infrared System (SBIRS), which uses satellite imagery to detect and track missiles. The probability that an intruding object (e.g., a missile) will be detected on a flight track by SBIRS is 0.6. Consider a sample of 10 simulated tracks, each with an intruding object. Let x equal the number of these tracks where SBIRS detects the object. Complete parts a through d.
Many primary care doctors feel overworked and burdened by potential lawsuits. In fact, a group of researchers reported medicine as a career. Let x represent the number of sampled general practice physicians who do not recommend medicine as a career. Complete parts a through d.
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