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Homework answers / question archive / HOMEWORK 13 PART B 1

HOMEWORK 13 PART B 1. A basketball player makes 75 % of the free throws he shoots. If he tries 8 free throws what is the probability that: (a) He will make exactly 2 throws? (b) He will make exactly 5 throws? (c) He will make either 2 or 5 throws? 2. A surgery has a success rate of 75%. Suppose that the surgery is performed on three patients. a. What is the probability that the surgery is successful on at least 2 patients? % b. On average, how many surgeries can we expect to be successful if performed on a group of three patients? c. What is the standard deviation of the number of successful surgeries performed on a group of three patients? • Your answers must be accurate to the nearest hundreth. 3. A basketball player makes 70% of the free throws he shoots. Suppose that he tries 15 free throws. a. What is the probability that he will make more than 7 throws? % b. How many baskets can the player expect to make if he takes 15 shots? c. What is the standard deviation of the number of successful free throws out of 15 total? • Your answers must be accurate to the nearest hundreth. 4. The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting Southwest flights and observing whether they arrive on time. (a) Find the probability that at least flights arrive late . (b) Would it be unusual for Southwest to have (Enter YES or NO) flights arrive late? 5. It is estimated that 75% of a grapefruit crop is good; the other 25% have rotten centers that cannot be detected until the grapefruit are cut open. The grapefruit are sold in sacks of 10. a. What is the probability of getting at least 9 good grapefruit in a sack? % b. If you purchase a sack of 10 grapefruit, how many can you expect to be good? c. What is the standard deviation of the number of good grapefruit in a sack of 10? • Your answers must be accurate to the nearest hundredth. 6. Joe is new to cooking. The probability that Joe burns dinner is . (a) What is the probability that in the next of them will burn? Express your dinners Joe prepares, answer as a decimal rounded to 4 decimal places after the decimal point. Answer: (b) What is the probability that in the next dinners Joe prepares, at least of them will burn? Express your answer as a decimal rounded to 4 decimal places after the decimal point. Answer: (c) What is the probability that in the next dinners Joe prepares, less than of them will burn? Express your answer as a decimal rounded to 4 decimal places after the decimal point. Answer: 7. Suppose that find is a random variable with a binomial distribution. If . Round your answer to 3 decimal places. and , 8. Suppose that a variable has a binomial distribution with of the variable? = 12 and = 0.01. What is the expected value = 20 and = 0.57. Expected value = 9. Suppose that a variable has a binomial distribution with Round your answer to 2 decimal places. (a) What is the expected value of the variable? Expected value = (b) What is the standard deviation of the variable? Standard deviation = 10. A quiz consists of 10 multiple-choice questions, each with 4 possible answers but only one is correct. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 55%. Note: Use up to 3 decimal places in your answers. 11. It is known that a certain hockey goalie will successfully make a save 86.03% of the time. Suppose that the hockey goalie attempts to make 11 saves. What is the probability that the hockey goalie will make at least 8 saves? Let be the random variable which denotes the number of saves that are made by the hockey goalie. Find the expected value and standard deviation of the random variable. 12. If is a binomial random variable, compute for each of the following cases: (a) (b) (c) (d) 13. If is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases: (a) (b) (c) (d) 14. Antibiotic for blood infections. Enterococci are bacteria that cause blood infections in hospitalized patients. One antibiotic used to battle enterococci is vancomycin. A study by a large nationwide health system revealed that % of all enterococci in its hospitals were resistant to vancomycin. Consider a random sample of four patients with blood infections caused by the enterococci bacterium. Suppose that all four patients are treated with the antibiotic vancomycin. Note: Give your answers in decimal form with at least four decimal places. a) What is the probability that all four patients are treated successfully? Answer: b) What is the probability that the bacteria resist the antibiotic in at least one patient? Answer: Note: A study by the Centers for Disease Control and Prevention on this subject was published in the New York Times, Sept. 12, 1995. 15. Consider an experiment in which identical small boxes are placed side by side on a table. A crystal is placed at random inside one of the boxes. A self-professed "psychic" is asked to pick the box that contains the crystal. a) If the psychic simply guesses, what is the probability that he/she picks the box with the crystal? Answer: b) If the experiment is repeated once?

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