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CHAPTER 5
Name: _______________
Part I: Multiple choice.
Circle the letter corresponding to the best answer choice.
1. Suppose that adult women in China have heights that are normally distributed
with mean 155 centimeters and standard deviation 8 centimeters. Adult women in
Japan have heights which are normally distributed with mean 158 centimeters and
standard deviation 6 centimeters. Which country has the higher percentage of
women taller than 167 centimeters?
(a) China
(b) Japan
(c) The percentages are the same.
(d) It is not possible to tell from the information given.
2. The mean of the normal curve above is
(a) 80
(b) 90
(c) 100
(d) 110
(e) 120
3. The standard deviation of the normal curve above is
(a) 5
(b) 10
(c) 15
(d) 20
(e) 25
4. For a normal distribution with mean 20 and standard deviation 5,
approximately what percent of the observations will be less than 10?
(a) 97.5% (b) 32%
(c) 16%% (d) 5%
(e) 2.5%
5. The distribution of heights of adult men is approximately normal with mean 69
inches and standard deviation 2.5 inches. How tall is a man whose standardized
height is 0.3?
(a) 68.25 inches
(b) 68.7 inches
(c) 69.3 inches
(d) 69.75 inches
(e) We can't tell without the normal table from the text.
6. The change in scales makes it hard to compare scores on the 1994 math SAT
(mean 470, standard deviation 110) and the 1996 math SAT (mean 500, standard
deviation 100). Jane took the SAT in 1994 and scored 500. Her sister Colleen took
the SAT in 1996 and scored
520. Who did better on the exam, and how can you tell?
(a) Colleen -- she scored 20 points higher than Jane.
(b) Colleen -- her standard score is higher than Jane's.
(c) Jane -- her standard score is higher than Colleen's.
(d) Jane -- the standard deviation was bigger in 1994.
(e) Can't tell from the information given.
Part II: Short answer questions.
7. Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. There are
1000 adult spiders in the colony, and their weights are normally distributed with
mean 11 grams and standard deviation 2 grams.
(a) About what percent of spiders in the colony weigh between 7 grams and 13
grams? (Sketch a normal curve and use the 68-95-99.7 rule.)
(b) What is the standard score of a spider in this colony that weighs 12 grams?
(c) About how many spiders in the colony weigh more than 12 grams?
8. At a certain fast food restaurant, automatic soft drink filling machines have been
installed. For 20-ounce cups, the machine has been set to dispense soda according
to a normal distribution with mean 18.5 ounces and standard deviation 0.6 ounces.
(a) Sketch a normal curve to illustrate the amount of soda dispensed by the
machine for 20-ounce cups. Be sure to label the mean and the points one, two,
and three standard deviations away from the mean.
(b) Use the 68-95-99.7 rule to estimate the percent of 20-ounce cups filled by this
machine that will have between 16.7 and 19.7 ounces of soda in them. Illustrate
your method clearly.
(c) What percent of 20-ounce cups filled by the machine will overflow (that is, get
more than 20 ounces of soda)?
(d) Calculate the 20th percentile of the soda dispensed distribution. Illustrate your
method clearly. Explain what this value means for consumers who order 20-ounce
sodas.