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The first Stat exam had a mean of 80 and a standard deviation of 4 points; the second had a mean of 70 and a standard deviation of 15 points. Reginald scored an 80 on the first test and an 85 on the second. Sara scored an 88 on the first but only a 65 on the second. Although Reginald's total score is higher, Sara feels she should get the higher grade. Explain her point of view.

Anna, a language major, took final exams in both French and Spanish and scored 83 on each. Her roommate Megan, also taking both courses, scored 77 on the French exam and 95 on the Spanish exam. Overall, student scores on the French exam had a mean of 81 and a standard deviation of \(5,\) and the Spanish scores had a mean of 74 and a standard deviation of 15 . a. To qualify for language honors, a major must maintain at least an 85 average for all language courses taken. So far, which student qualifies? b. Which student's overall performance was better?

Two companies market new batteries targeted at owners of personal music players. DuraTunes claims a mean battery life of 11 hours, while RockReady advertises 12 hours. a. Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to buy. b. Suppose those standard deviations are 2 hours for DuraTunes and 1.5 hours for RockReady. You are headed for 8 hours at the beach. Which battery is most likely to last all day? Explain. c. If your beach trip is all weekend, and you probably will have the music on for 16 hours, which battery is most likely to last? Explain.

Using \(N(1152,84)\), the Normal model for weights of Angus steers in Exercise 13 a. How many standard deviations from the mean would a steer weighing 1000 pounds be? b. Which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?

John Beale of Stanford, California, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a two-month period. These are 100 representative readings.) a. How many standard deviations from the mean would a car going under the speed limit be? b. Which would be more unusual, a car traveling 34 mph or one going 10 mph?

More cattle Recall that the beef cattle described in Exercise 29 ?had a mean weight of 1152 pounds, with a standard deviation of 84 pounds. a. Cattle buyers hope that yearling Angus steers will weigh at least 1000 pounds. To see how much over (or under) that goal the cattle are, we could subtract 1000 pounds from all the weights. What would the new mean and standard deviation be? b. Suppose such cattle sell at auction for 40 cents a pound. Find the mean and standard deviation of the sale prices (in dollars) for all the steers.

For the car speed data in Exercise 30 ?, recall that the mean speed recorded was \(23.84 \mathrm{mph},\) with a standard deviation of \(3.56 \mathrm{mph}\). To see how many cars are speeding, John subtracts 20 mph from all speeds. a. What is the mean speed now? What is the new standard deviation? b. His friend in Berlin wants to study the speeds, so John converts all the original miles-perhour readings to kilometers per hour by multiplying all speeds by 1.609 (km per mile). What is the mean now? What is the new standard deviation?

A popular band on tour played a series of concerts in large venues. They always drew a large crowd, averaging 21,359 fans. While the band did not announce (and probably never calculated) the standard deviation, which of these values do you think is most likely to be correct: \(20,200,2000,\) or 20,000 fans? Explain your choice.

Exercise 10 proposes modeling IQ scores with \(N(100,15)\). What IQ would you consider to be unusually high? Explain.

A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model applies. a. Draw the Normal model for tree diameters. b. What size would you expect the central \(95 \%\) of all trees to be? c. About what percent of the trees should be less than an inch in diameter? d. About what percent of the trees should be between 5.8 and 10.4 inches in diameter? e. About what percent of the trees should be over 15 inches in diameter?