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STATISTICS 101 section 2
Quiz 3
This is a multiple choice and short answer quiz. If you erase, erase completely. Don’t
spend too much time on any single question. All blanks have equal weight unless otherwise
stated.
You may use a calculator. All numerical answers must be accurate to two decimal places.
Don’t start until you are told so.
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1. [2 pts] Among freshmen at Duke, scores on the math SAT followed the normal curve
with an average of 480 and an SD of 70.
(a) A student who scored 585 on the math SAT was in what percentile of the score
distribution for Duke?
The stand unit (z transform) is (585 − 480)/70 = 1.5. The percentage of the
population below 1.5 is 0.8664 + (1 − 0.8664)/2 = 0.9332
(b) A quarter of the class got lower scores on the math SAT than what value?
From the table, the 25th percentile of the standard normal distribution is around
-0.70 (or -0.675). Therefore, the 25th percentile of the score distribution is 480 −
0.7 × 70 = 431.
2. [3 pts] A standard deck of 52 cards is shuffled, two cards are dealt. (without replacement)
(a) What is the probability that the first card is a Queen or a diamond?
Define event A = the first card is Queen and event B = the first card is a
diamond.
P (A or B) = P (A) + P (B) − P (A and B) =
4
13
1
16
+
−
=
= 0.31
52 52 52
52
(b) What is the probability that the second card is a two given that the first card is
one of face cards (Aces, Kings, Queens or Jacks)?
4
51
(c) What is the probability that all two cards are diamonds?
13 12
×
= 0.06
52 51
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3. [3 pts] True of False:
(a) The regression line for y on x estimates the average value of y corresponding to
each value of x.Ans: True
(b) The slope of SD line is -(SD of y)/(SD of x) when r is negative. Ans: True
(c) In a series of scatter diagrams with the same SDs, as r get closer to 0, the points
cluster more tightly around a line. Ans: False
4. [4 pts] You want to predict the metabolic rate of an animal from its body mass (in
kilograms). You draw a sample of 50 animals and find that the estimated slope is -0.4
and the estimated intercept is 100. The mean body mass is 150 kg and the SD of the
body mass is 80kg. The SD of the metabolic rate is 40.
(a) What is the correlation coefficient?
From the regression line equation, −0.4 = r × 40/80. Hence r = −0.8
(b) What percentage of the variation in metabolic rate as a function of body mass
is explained by the regression line?
R2 = (−0.8)2 = 0.64. 64% of the variation in metabolic rate as a function of
body mass is explained by the regression line
(c) What is the mean heart rate?
average of y = 100 − 0.4 × 150 = 40
(d) About the 96% of the data will fall within what vertical distance of the regression
line?
The r.m.s. error for regression is
p
1 − r2 SD of y =
√
1 − 0.64 × 40 = 24
From the table, 96% of the standard normal distribution fall within 2 SD. Therefore, the 96% of the data will fall within 24 × 2 = 48 vertical distance of the
regression line.
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