Probability and Statistics Test – Chapter 8
Name __________________________________

Formulas:  x 
n
N n
N 1
Standard deviation of sample means for finite populations.

x 
z
*
Period ______
Standard deviation for sample means from a very large population.
n
x 
Central Limit Theorem (z-score)

n
x 
 x   
2
x
number of samples
Standard deviation of sample means
Fill in the blank:
1. What does each symbol represent?
µ: _______________________________________________
 x : ______________________________________________
σ: _______________________________________________
 x : ______________________________________________
2. As the population size of N gets larger and larger, the value of
3. What do the following represent?
N: ______________________________________
n: _______________________________________
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N n
gets very close to _____________.
N 1
4. The larger the sample size, the ____________________ the standard deviation (error) of the sample means
will be.
5. Population = {9, 14, 33, 42}
a. Find the mean, µ, and the standard deviation, σ, of the population.
b. Make a list of all possible samples of size 2 that can be drawn from the population. Determine the mean of
each of these samples and form a sampling distribution of these samples.
Size 2
x
x   x 
x   x 2
c. Find the mean,  x , of the sampling distribution.
d. Find the standard deviation,  x , of this sampling distribution.
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6. If the standard deviation of 500,000 numbers is 50, what is the standard deviation of the means of the
samples of size 30?
7. The mean number of workers employed by each McDonald’s restaurant is 49.1, with a standard deviation of
7.2. If a random sample of 50 restaurants is taken, what is the probability that the average number of
workers among the samples exceeds 51?
8. A certain farm cooperative claims that the average weight of its packaged bags of potatoes is 80 ounces with
a standard deviation of 4 ounces. To check the accuracy of the stated weight, a local consumer’s complaint
bureau official selects a random sample of 35 bags of potatoes. Within what limits should 95% of these bags
lie?
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9. In Macon County the mean number of years served in prison by persons convicted of second-degree murder
is 12.4 with a standard deviation of 2.8 years. If a sample of 50 such persons is to be selected, what is the
probability that the sample mean time spent in prison:
a. is less than 13 years?
b. lies between 12.0 and 12.6 years?
10. Each refrigerator that is manufactured in the United States has a serial number. After a series of complaints
about defective thermostats one of the manufacturers has decided to randomly check 15 refrigerators sold in
Chicago. According to company records, refrigerators sold in Chicago during 2012 had serial numbers
whose last five digits were between 30,000 and 71,000. If column 10 of Table VI is used, which
refrigerators will be checked?
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11. There are 2250 students at PVHS. We would like to select 20 students at random to conduct a survey.
Using the table of random digits, list 20 randomly selected values using columns 3, 4, 5, and so on.
12. The mean time that it takes a particular anesthetic drug to produce unconsciousness is 11.5 minutes with a
standard deviation of 1.8 minutes. If a random sample of 40 patients is to be selected, what is the
probability that x will be less than 12.0 minutes?
13. What is the standard deviation of the numbers 21, 34, 56, 67, and 76?
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14. If the mean of a population of 300,000,000 is 80, if the standard deviation is 15, and if samples are taken,
approximately what is the standard deviation of the means of samples:
a. of size 10?
b. of size 50?
c. of size 200?
d. of size 1000?
15. The following are the number of students in 10 different classes.
{24, 30, 25, 12, 18, 12, 31, 28, 15, 23}. Samples of size 3 are taken.
Find:  x = _______________________
 x = ________________________
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