ST 311 Midterm: ST 311 NCSU Exam1 311
ST 311 ReilandPRACTICE PROBLEMS FOR EXAM 1
Topics covered on Exam 1 : Chapters 1-8, 10, 11 in text.
This material is covered in webassign homework assignments 1 through 4
Exam information: 90 minute time limit; materials allowed: calculator (no laptops), 1 8 x11 sheet of
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paper (2 sided)with notes, definitions, formulas, etc. Normal table will be provided with the exam.
WARNING! The problems below may not cover all topics for which you are responsible on exam 1.
Note: the exam will have a mix of multiple choice and numerical answer questions.
Answers are at the end of the document.
1. (normal model) The heights of American men aged 18 to 24 can be described by a Normal model with mean
68 inches and standard deviation 2.5 inches. Half of all young men are shorter than
a) 65.5 inches b) 68 inches c) 70.5 inches d) can't tell because the median height is not given
2. (68-95-99.7 rule) Use the information in Problem 1 and the to determine the percentage of68-95-99.7 rule
young men that are taller than 6' 1".
3. (numerical summaries) The grade point averages (GPA) of 7 randomly chosen students in a statistics class
are
3.14 2.37 2.94 3.60 1.70 4.00 1.85
Find these statistics:
a) mean
b) median and quartiles
c) range and IQR
4. (sample standard deviation) Refer to the information given in the previous problem. If
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what is the sample standard deviation ?=
5. (z-scores) A standardized test designed to measure math anxiety has a mean of 100 and a standard deviation
of 10 in the population of first year college students. Which of the following observations would
you suspect is an outlier?
a) 150 b) 100 c) 90 d) 125 e) none of the above
6. (numerical summaries) A clerk entering salary data into a company spreadsheet accidentally put an extra “0”
in the boss's salary, listing it as $2,000,000 instead of $200,000. Explain how this will affect these summary
statistics for the company payroll:
a) measures of center: mean and median
b) measures of spread: range, IQR, and standard deviation
7. (histogram) The distribution represented by the histogram below is:
f |
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ST 311 Practice Problems Exam 1 page 2
--------------------------------------------------------------------------- X
0 1 2 3 4 5 6 7 8 9 10
Choose one of the following:
a) skewed to the right.
b) skewed to the left.
c) symmetric.
d) normal.
8. (quartiles, box plots) Twenty-seven applicants interested in working for the Food Stamp program took an
examination designed to measure their aptitude for social work. The following test scores were obtained:
79, 93, 84, 86, 77, 63, 46, 97, 87, 88, 87, 92, 68, 72, 86, 98, 81, 70, 66, 98, 59, 76, 68, 91, 94, 85, 88.
a. Find . U"
b. Construct a boxplot for these observations. Do you observe any outliers?
9. (normal model, inverse problem) A manufacturer of television sets has found that for the sets he produces,
the lengths of time until the first repair can be described by a normal model with a mean of 4.5 years and a
standard deviation of 1.5 years. If the manufacturer sets the warrantee so that only 10.2% of the 1st repairs
are covered by the warrantee, how long should the warrantee last?
10. (normal model) Suppose the amount of tar in cigarettes is described by a normal model with a mean of 3.5
mg and a standard deviation of 0.5 mg.
a. What proportion of cigarettes have a tar content that exceeds 4.25 mg?
b. In order to advertise as a low tar brand, a manufacturer must prove that their tar content is below the
25th percentile of the tar content distribution. Find the 25th percentile of the distribution of tar amounts.
11. (2-way tables) Has the percentage of young girls drinking milk changed over time? The following table is
consistent with the results from “Beverage Choices of Young Females: Changes and Impact on Nutrient
Intakes” (Shanthy A. Bowman, Journal of the American Dietetic Association, 102(9), pp. 1234-1239):
Nationwide Food Survey Years
1987-1988 1989-1991 1994-1996
Drinks Fluid Milk Yes 354 502 366
No 226 335 366
Total
1222
927
Total 580 837 732 2149
a. Find the following:
1. What percent of the young girls reported that they drink milk?
2. What percent of the young girls were in the 1989-1991 survey?
3. What percent of the young girls who reported that they drink milk were in the 1989-1991 survey?
4. What percent of the young girls in 1989-1991 reported that they drink milk?
b. What is the marginal distribution of milk consumption?
12. (Simpson's paradox) It's the last inning of an important baseball game. The home team is losing by a run,
the bases are loaded and the manager needs a pinch hitter. Two batters are available to pinch hit. Here are
their statistics:
33 for 103 28 for 81 5 for 22
45 for 151 12 for 32 33 for 119
Player Overall vs Left-handed pitching vs Right-handed pitching
A
B
Based on their overall batting averages and their batting averages against right-handed and left-handed
pitchers, who would you select as the pinch hitter? What is this phenomenon called?
13. (normal model) The mean SAT verbal score of next year's freshmen entering the local university is 600. It is
also known that 69.5% of these freshmen have scores that are less than 625. If the scores can be described
by a normal model, what is the standard deviation of the scores?
ST 311 Practice Problems Exam 1 page 3
14. (z-scores) Two students are enrolled in an introductory statistics course at the University of Florida. The
first student is in a morning section and the second student is in an afternoon section. If the student in the
morning section takes a midterm and earns a score of 76, while the student in the afternoon section takes a
midterm with a score of 72, which student has performed better compared to the rest of the students in his
respective class? Assume that the test scores can be described by a normal model. For the morning class,
the class mean was 64 with a standard deviation of 8. For the afternoon class, the class mean was 60 with a
standard deviation of 7.5.
15. (z-score, meaning) Suppose that a Normal model describes the acidity (pH) of rainwater, and the water
tested after last week's storm had a z-score of 1.8. This means that the acidity of that rain
a. had a pH of 1.8
b. varied with a standard deviation of 1.8
c. had a pH 1.8 higher than the average rainfall
d. had a pH 1.8 times that of average rainwater
e. had a pH 1.8 standard deviations higher than that of average rainwater
16. (linear transformation) The highway gas mileage , measured in miles per gallon (mpg), of 26 models ofB
midsize cars, have the following summary statistics: 26.54 mpg, median 26 mpg, 3.04 mpg,Bœ œ =œ
IQR œBB3 mpg. If you convert gas mileage from miles per gallon to which is measured in miles per
8/A
liter, what are the new values of the summary statistics? (3.785 liters 1 gallon).œ
17. (normal probability plot) Shown below is the normal probability plot for 200 monthly telephone bills.
Norm al Quantile Plot
0
20
40
60
80
10 0
12 0
14 0
-4 -3 -2 -1 0 1 2 3 4
z-score
phone bills
Shown below is a histogram. Is this a histogram of the same data that was used to construct the normal
probability plot?
Histogram
0
10
20
30
40
Frequency
Document Summary
This material is covered in webassign homework assignments 1 through 4. Exam information: 90 minute time limit; materials allowed: calculator (no laptops), 1 8 x11 sheet of paper (2 sided)with notes, definitions, formulas, etc. Normal table will be provided with the exam. The problems below may not cover all topics for which you are responsible on exam 1. Note: the exam will have a mix of multiple choice and numerical answer questions. Answers are at the end of the document. (normal model) the heights of american men aged 18 to 24 can be described by a normal model with mean. Half of all young men are shorter than a) 65. 5 inches b) 68 inches c) 70. 5 inches d) can"t tell because the median height is not given (68-95-99. 7 rule) use the information in problem 1 and the young men that are taller than 6" 1".
