Stat 10, UCLA
Chapter 5 Solutions
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.
18 scores were actually within 1.25 SDs of the average, or within
the range (37.5, 62.5).
In 1967, a score of 600 was about 1.22 SDs above the average, and
the percentage scoring over 600 was about 11%.
In 1994, a score of 600 was about 1.61 SDs above the average, and
the percentage scoring over 600 was about 5%.
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.
- 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.
- 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.
- False. See page 92. Adding a constant to the data does not change
- True. All deviations from the average are doubled.
- False. The deviations from the average will also have their signs
changed, but negatives go away in the squaring. Besides, SD
is never negative.
- False. The list 10, 11, 60 has a median of 11 but an average of 27.
- False again. For the list 10, 11, 60, two-thirds of the entries
are below the average.
- False. Income data doesn't follow the normal curve even with large
samples, because incomes aren't measured below 0. See page 88.
- 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.
- (i) is the correct one. hint: number of courses taken must be >= 0