Stat 10, UCLA

Chapter 5 Solutions

1. The Normal Table in the back of the book shows that about 79% of the area falls between -1.25 and 1.25. For 25 test scores, 79% = (about) 20.
2. 18 scores were actually within 1.25 SDs of the average, or within the range (37.5, 62.5).

1. In 1967, a score of 600 was about 1.22 SDs above the average, and the percentage scoring over 600 was about 11%.
2. In 1994, a score of 600 was about 1.61 SDs above the average, and the percentage scoring over 600 was about 5%.

1. 20%
2. 12%

1. The percentage of men with heights between 66 inches and 72 inches is exactly equal to the area between 66 inches and 72 inches under the histogram. This percentage is approximately equal to the area between -1 and 1 under the normal curve.

1. 350 is 1.5 SDs below the average. This student is at the 7th percentile of the score distribution because under the normal curve, 7% of the area lies below -1.5.
2. About 75% of the area under the normal curve lies below 0.7 SDs, so a student needs a score of about 570 on the Math SAT to be at this percentile.

1. True
2. False. See page 92. Adding a constant to the data does not change the spread.
3. True
4. True. All deviations from the average are doubled.
5. True
6. False. The deviations from the average will also have their signs changed, but negatives go away in the squaring. Besides, SD is never negative.

1. False. The list 10, 11, 60 has a median of 11 but an average of 27.
2. False again. For the list 10, 11, 60, two-thirds of the entries are below the average.
3. False. Income data doesn't follow the normal curve even with large samples, because incomes aren't measured below 0. See page 88.
4. False. If they both follow the normal curve, then you might get about 68% of the area between 40 and 60 for both lists. But that is still only an approximation, and there are many other possibilities.

2. (i) is the correct one. hint: number of courses taken must be >= 0

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