MA 141 Midterm: MA 141 NCSU Exam1 305
ST 305 ReilandPRACTICE PROBLEMS FOR EXAM 1
Topics covered on Exam 1 : Chapters 1-10 in text.
This material is covered in webassign homework assignments 1 through 4 and worksheets 1-15.
Exam information: materials allowed: calculator (no laptops), one 3 x 5 notecard (2 sided)with notes,
definitions, formulas, etc. Standard 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.
Answers are at the end of the document.
1. The distribution of heights of American men aged 18 to 24 can be approximated 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. Use the information in Problem 1 and the to determine the percentage of young men that are68-95-99.7 rule
taller than 6' 1".
3. 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. Refer to the information given in the previous problem. If ( 4.51, what is the standard
CC œ)
#
deviation?
5. 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. 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. The distribution represented by the histogram below is:
f |
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|---- | | | |----- | -
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--------------------------------------------------------------------------- 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.
ST 305 Practice Problems Exam 1 page 2
8. 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. A manufacturer of television sets has found that for the sets they produce, the distribution of lengths of time
until the first repair can be approximated 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. Suppose the distribution of the amount of tar in cigarettes can be approximated 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. 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. 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. 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 distribution of scores can be
approximated by a normal model, what is the standard deviation of the scores?
14. 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 both distributions of test scores can be approximated 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. 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
ST 305 Practice Problems Exam 1 page 3
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. The highway gas mileage , measured in miles per gallon (mpg), of 26 models of midsize cars, have theB
following summary statistics: 26.54 mpg, median 26 mpg, 3.04 mpg, 3 mpg. If youBœ œ =œ œIQR
convert gas mileage from miles per gallon to which is measured in miles per liter, what are the newBB
8/A
values of the summary statistics? (3.785 liters 1 gallon).œ
17. Shown below is the normal probability plot for 200 monthly telephone bills.
Normal 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 and worksheets 1-15. Exam information: materials allowed: calculator (no laptops), one 3 x 5 notecard (2 sided)with notes, definitions, formulas, etc. Standard normal table will be provided with the exam. The problems below may not cover all topics for which you are responsible on exam 1. Answers are at the end of the document: the distribution of heights of american men aged 18 to 24 can be approximated 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: use the information in problem 1 and the. 68-95-99. 7 rule to determine the percentage of young men that are taller than 6" 1": the grade point averages (gpa) of 7 randomly chosen students in a statistics class are.
