Practice Sheet – Chance Variability in Sampling
1. A box contains 80 red marbles and 20 blue marbles. A random sample of 25
marbles is drawn from the box without replacement. What is the probability of
getting exactly 20 red marbles.
2. The average weight of adult males is 170lb with a standard deviation of 25lb. If
a random sample of 10 adult males gets on an elevator, what is the probability that
the total weight of the males will exceed the 2000lb load capacity of the elevator?
3. Of the 3600 WFU students, 35% are in-state students. If a random sample of 900
WFU students is chosen, what is the probability that the percent of in-state
students in the sample is between 33% and 37%?
4. The average SAT score in N.C. last year was 890 with a standard deviation of 210.
(a) If a random sample of 25 SAT scores from N.C. is taken, what is the
probability that the average SAT score of the sample is greater than 900?
(b) Same question as (a) except sample size is 400.
(c) Same question as (a) except sample size is 1600.
5. According to the American Red Cross, 37% of the population have O+ blood type.
If a random sample of 400 donors attend a blood drive, what is the probability that
the percent of O+ blood types in the sample is greater than 40%?
6. A group of 50,000 tax forms shows an average gross income of $37,000 with a
standard deviation of $20,000. Also, 20% of the forms show a gross income over
$50,000.
(a) If a random sample of 400 tax forms is taken, what is the probability that
between 19% and 21% of the sample show gross incomes over $50,000?
(b) If a random sample of 25 tax forms is taken, what is the probability that the
average gross income of the sample is less than $35,000?
7. The average IQ score on the Stanford-Binet Intelligence Test is 100 with a
standard deviation of 15. Assume that IQ scores are normally distributed.
(a) What percent of all IQ scores would be greater than 121?
(b) If a random sample of 400 IQ scores is taken, what is the probability that more
than 10% of the sample scores would be greater than 121?
(c) If a random sample of 25 IQ scores is taken, what is the probability that the
average IQ of the sample is less than 105?
8. A box contains 400 marbles, some are red and the rest are blue. A random sample
of 100 marbles is drawn from the box without replacement. There are 68 red
marbles in this sample. Construct, if possible, a 95% confidence interval for the
percent of red marbles in the original box.
9. A quality control technician wishes to estimate the average weight of widgets in a
large shipment. She takes a random sample of 16 widgets and finds the average
weight to be 120g with SD of 15g. Construct, if possible, an 80% confidence
interval for the average weight of all the widgets in the shipment.
10. There are 2700 institutions of higher learning in the U.S. Suppose that a random
sample of these institutions is chosen and the average enrollment of this sample is
3700 with SD of 6500.
(a) If the sample size is 400, construct if possible a 95% confidence interval for
the average enrollment of all 2700 institutions.
(b) Repeat (a) if the sample size is 64.
11. In a certain town, there are 25,000 households. A simple random sample of 500
households is taken. 179 of the sample households had dishwashers, and 498 had
refrigerators.
(a) Construct, if possible, a 95% confidence interval for the percent of all 25,000
households with dishwashers.
(b) Repeat (a) for refrigerators.
12. A quality control technician wishes to estimate the nicotine content of the
cigarettes produced by a tobacco company. She takes a random sample of 7
cigarettes and gets the following nicotine contents (in mg): 16, 17, 19, 20, 20,
21, and 22. Construct if possible a 90% confidence interval for the average
nicotine content of all the cigarettes produced by the company.
Solution Key for Chance Variability in Sampling
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22%
.007%
85%
(a) 40.5%
(b) 17%
(c) 3%
11%
(a) 38%
(b) 31%
(a) 8%
(b) 7%
(c) 95.5%
60.12% to 75.88%
114.8g to 125.2g
(a) 3115 to 4285
(b) 2120 to 5280
(a) 31.6% to 40.0% (b) 99.05% to 100.15% (cannot do!)
17.7 mg to 20.9 mg