Name: ________________
Grade: _______
Math 223 Exam 1
Good Luck!
Multiple Choice Section – Select the choice that best answers the problems below.
(1.5 points each)
1. Determine whether the given value is a statistic or a parameter.
A sample of Dall sheep is measured to have a mean horn length of 35.7 inches.
2. Determine whether the given value is from a discrete or a continuous data set.
In studying the Loggerhead turtle on Anna Maria Island, FL, scientists observe the number of
hatchlings in all 253 nests.
3. Determine whether the given value is qualitative or quantitative.
Physicians rank the severity of asthma using mild intermittent asthma, mild persistent asthma,
moderate persistent asthma, severe persistent asthma, or brittle asthma.
4. Determine whether the description below corresponds to an observational study or an
experiment.
In a study of the Bald Eagle population, the number of breeding pairs is counted.
5. Select the pair of events that are disjoint for a single trial.
a) Randomly selecting a cardiac surgeon; Randomly selecting a female physician
b) Randomly selecting a subject who opposes all cloning; Randomly selecting a subject who
approves of cloning of sheep
c) Randomly selecting someone taking Vitamin C; Randomly selecting someone with a cold
d) Randomly selecting a hairdresser; Randomly selecting a male
6. Select a pair of events that are independent.
a) Randomly selecting a rose; Randomly selecting a flower with red petals.
b) Consuming a 1400 calorie hamburger each day for a week; Gaining weight
c) Randomly selecting someone who gets this question correct; Randomly selecting someone who
gets a perfect score on this exam
d) Randomly selecting someone with type A blood; Randomly selecting someone with type O
blood
7. Select the procedure that does NOT result in a binomial distribution.
a) Recording the genders of 250 newborn babies
b) Surveying married couples and asking them how many children they have
c) Surveying college students and asking them if they ate breakfast today
d) Surveying students in this class and asking them if they think that they got this question correct
8. Use the Standard Normal distribution to answer the following question.
Identify the probability corresponding to z-scores between -2.04 and 1.67.
a) .9525
b) .0207
c) .9318
d) .9732
Short Answer Section – Remember to show/justify your work where appropriate.
(The point value for each question is given after each question.)
Use the following sample data to answer the following four questions.
Henry Cavendish once attempted to measure the density of Earth using a torsion balance. In the table
below are 29 observations sorted by value. Each value is in terms of the density of water, so a value
of 5.79 would indicate Earth is 5.79 times as dense as water.
4.88
5.36
5.58
5.07
5.39
5.61
5.10
5.42
5.62
5.26
5.44
5.63
5.27
5.46
5.65
5.29
5.47
5.68
5.29
5.50
5.75
5.30
5.53
5.77
5.34
5.55
5.79
9. The sum of the 29 observations is 157.91. What is the mean of these observations? (2 pts)
10. Find the five number summary for this sample. (6 pts)
11. Find the sample data value corresponding to P15. (4 pts)
12. This data set is skewed to the left. Explain how we know this. (3 pts)
5.34
5.57
13. To monitor levels of the giardia parasite in the Rio Grande, aquatic biologists collect test tube
samples at various locations determined by a computer randomization program. Does this
sampling plan result in a non-simple random sample or a simple random sample? Why? (4 pts)
14. Explain in your own words what the variance (or the standard deviation) measures. (4 pts)
Use the frequency distribution below to answer the next four questions.
A sample of 80 juvenile salmon is grouped into the resulting relative frequency distribution based on
their weights.
Weight (in grams)
100-149
150-199
200-249
250-299
Relative Frequency
0.1875
0.125
0.375
0.3125
15. What is the class width? (2.5 pts)
16. If a frequency distribution were constructed for the weights of these juvenile salmon, what would
be the frequency for the class with weights of 250-299 g? (2.5 pts)
17. If a cumulative frequency distribution were constructed for the weights of these juvenile salmon,
what would be the cumulative frequency for the class with weights of less than 250 g? (3 pts)
Use the sample data below for the following three questions. (3 pts each)
Biologists studying the re-vegetation of two species of succulent plants in the South African desert
examined the number of plants that survived depending on whether they were planted in multi-species
clumps or planted alone. The following data resulted:
# of Species 1 that survived
Planted in Multi-Species
Clumps
64
# of Species 2 that survived
34
Planted Alone
87
47
18. If one of the surviving succulent plants is randomly selected, find the probability of getting a
surviving plant that was planted in a multi-species clump.
19. If one of the surviving succulent plants is randomly selected, find the probability of getting a
surviving plant that was Species 2 or was planted alone.
20. If two different surviving succulent plants are randomly selected, find the probability that they both
were Species 1.
21. Suppose the heights for each sex are normally distributed, with means of 70 inches for men and 65
inches for women, and with standard deviations of 3 inches for men and 2.5 inches for women.
Pete is 72 inches tall and Jill is 67 inches tall. Who has the higher relative height? (Remember to
support your answer.) (4 pts)
Use the data below for the following four questions.
Dental researchers found the following probability values for the dental habits of the age, X, at which
children begin brushing their teeth and gums.
X
0
1
2
3
4
P(X)
.04
.19
.22
?
.31
22. What is the probability that a child begins brushing his/her teeth and gums at age 3? (3 pts)
23. What is the probability that a child is at least 2 years old when he/she begins brushing his/her teeth
and gums? (3 pts)
24. The average age at which children begin brushing their teeth and gums is 2.59 years. Calculate the
variance, V(X), of this probability distribution. Recall V  X    x 2  Px   2 . (4pts)


25. Calculate the standard deviation,  X , of this probability distribution. (2 pts)
Use the following information for the next three questions.
A particular type of tennis racket comes in a midsize version and an oversize version. Suppose that at
a certain store, 85% of all customers purchasing a racket want the midsize version.
26. Find the probability that exactly 15 of the next 20 rackets sales are midsize rackets.
(4 pts)
27. Find the standard deviation for the number of midsize rackets sold out of the next 20 racket sales.
(4 pts)
28. Find the expected number of oversize rackets sold out of every 60 racket sales. (3 pts)
29. Seniors at a public school who take a placement test have scores that are normally distributed with
a mean of 280 and a standard deviation of 40. Seniors at a private school who take the same test
have scores that are normally distributed with a mean of 310 and a standard deviation of 60. What
percent of private school seniors score higher than the average public school senior? (5 pts)
Use the following information to answer the next three questions.
Cockpits of fighter jets were originally designed for men only, so various changes are required to
better accommodate the new women pilots. In particular, engineers are redesigning the fighter jet
ejection seats. Before women became fighter jet pilots, the ACES-II ejection seats were designed for
men weighing between 140 lb and 211 lb. The population of women has normally distributed weights
with a mean of 143 lb and a standard deviation of 29 lb (based on data from the National Health
Survey).
30. Under the current ejection seat design, what is the probability that a particular woman’s weight is
too small to be safely protected? (4 pts)
31. If a sample of 50 women is randomly selected, find the probability that their mean weight exceeds
150 lbs? (5 pts)
32. If the engineers wish to design the new ejection seats so that only 15% of women’s weights are too
low to be safely protected, what should be the new lower bound for the new seats? (5 pts)
33. State the conditions under which the Central Limit Theorem can be applied. (5 pts)