Download Unit #13 Practice Test – Statistics

Name _________________________________________________D ate ________________ Period __________
Unit #13 Practice Test – Statistics
Things to Remember
**If you’re looking for a probability that is the “upper”
or more you subtract the probability from 1
**Within ___Standard Deviations
**The area under the curve = 1
-
68% of the distribution lies within one
standard deviation
95% of the distribution lies within two
standard deviations
99.7% of the distribution lies within three
standard deviations
** The bigger the standard deviation is, the WIDER the
graph is.
Practice Questions:
1. What are the mean, median, mode, and standard
deviation of the following: 6.5, 5.8, 3.9, 5.7, 4.2
2. During league play last Friday evening the scores of
the last 12 games bowled were 186, 165, 193, 216,
174, 184, 187, 209, 198, 143, 217 and 192. Create
the normal distribution curve for this data.
3. The mean score on a quiz is 82% with a standard
deviation of 4. Estimate the percent of scores what
were 90% or higher.
4. A psychology professor gives a 100 item true/false
test in a large college class. The mean score is 75.2
and the standard deviation is 8.1. The scores follow
a normal distribution. What is the minimum score
that is in the 99th percentile?
5. The exam scores of 200 students are distributed
normally with a mean of 72 and a standard
deviation of 10. Determine the number of students
that score between a 72% and a 82%.
Name _________________________________________________D ate ________________ Period __________
6. A population of adult males had their heights
measured. The heights were normally distributed.
Approximately what percentage of the heights,
rounded to the nearest whole number, are within
one standard deviation of the mean?
9. A normally distributed data set of 600 values has a
mean of 18.5 and a standard deviation of 3.25.
a. What is the approximate number of
values in the data set expected to be 22
or greater?
b. What is the approximate number of
values in the data set expected to be 16
or fewer?
7. At a company, the data set containing the ages of
applicants for a particular job was normally
distributed. The mean age of the applicants was 30
years old, and the standard deviation of the data set
was 3.5 years old. Which is closest to the percent of
applicants that were 21 years old or younger?
c. Which is closest to the expected
number of values in the data set that lie
between 21 and 27?
10. In a normal distribution, what is the probability that
a data value will fall above the data value
associated with a z-score of 0.28?
8. A normally distributed data set of 500 values has a
mean of 35 and a standard deviation of 7. Which is
closest to the probability that a value in the data set
will fall between 42 and 46?
11. A tire company claims that its tires have a mean
lifespan of 40,000 miles. If the standard deviation
for the company is 1,000 miles, what is the
probability that the tires will last 37,000 or more
but less than or equal to 43,000 miles?
Name _________________________________________________D ate ________________ Period __________
12. In a normal distribution, what is the probability that
a data value will fall below the data value
associated with a z-score of 2.39?
13. The graph below shows the normal probability of
the lifetime of an energy-efficient light bulb in
years. What is the mean?
14. What is the total area under a normally distributed
curve?
15. True or false – The smaller the standard deviation,
the wider the graph.
16. What is the percentage associated with the
percentage of data that falls below the data value
associated with a z-score of 0.64? Draw a quick
sketch.
17. A company observes the lifespan of 320 batteries
and finds that their data follows a normal
distribution. What is the approximate number of
batteries that fall within two standard deviations
from the mean?
18. A JFHS, the ages of all employees during the last 10
years are normally distributed. It has been
calculated that 95% of the ages fall between 24.1
and 64.2 years. What is the standard deviation of
the data?
19. The data Joseph collected while studying the
growth of a certain type of fungus is normally
distributed. Fungus A covered 23.4 square inches
during the given time. The mean growth was 19
square inches and the standard deviation was 1.7
square inches. What percent of the population
covered less surface area than Fungus A?
Name _________________________________________________D ate ________________ Period __________
20. The mean annual police officer’s salary in Virginia is
$36,500 and the standard deviation is 18,000.
Bedford county has a mean officer’s salary of
$47,000. What percent of the police departments
pay a lower mean annual salary than Bedford Co?
Factor completely.
23. 343𝑥 3 − 125
24. 9𝑥 3 − 35𝑥 2 + 24𝑥
21. Polly and Dolly live in different states. They both
took the SAT in their state – both states use a
grading system that was normally distributed. Polly
received a 1230 and the mean score for her state
was 1100 with a standard deviation of 67. Dolly
received a 450 and the mean score for her state
was a 400 with a standard deviation of 35. Is it true
that they both scored above the 75th percentile?
25. 18𝑟 2 𝑠 3 − 30𝑟𝑠 2
26. 4𝑥 2 + 19𝑥 − 30
22. Suppose that SOL scores among freshman are
normally distributed with a mean of 400 and a
standard deviation of 70. Approximately what
percent of freshman score between a 370 and a
440?
27. 8𝑥 4 + 𝑥