Download Test 1 from Fall - Marietta College

Name: ________________
Grade: _______
Math 223 Exam 1 Fall ‘07
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 study involves attaching altimeters to individual frigate birds, and their mean altitude is found to
be 226 meters.
2. Determine whether the given value is from a discrete or a continuous data set.
A sample of broad-billed hummingbirds is observed and their mean length is 3 inches.
3. Determine whether the given value is qualitative or quantitative.
Scientists classify the four major deserts in North America using different regions: the Great
Basin, the Mojave, the Sonoran, and the Chihuahuan.
4. Determine whether the description below corresponds to an observational study or an
experiment.
In a study of cold symptoms, the body temperatures of study participants were taken.
5. Select the pair of events that are disjoint for a single trial.
a) Randomly selecting a ophthalmologist; Randomly selecting a male doctor
b) Randomly selecting a bird; Randomly selecting a hummingbird
c) Randomly selecting someone with type O blood; Randomly selecting someone with Rh
positive blood
d) Randomly selecting someone taking Tylenol; Randomly selecting someone in a control group
taking no medications
6. Select a pair of events that are independent.
a) Randomly selecting a zebra; Randomly selecting an animal with stripes
b) Randomly selecting a dog; Randomly selecting a bird
c) Randomly selecting a tiger; Randomly selecting a member of the cat family
d) Randomly selecting an elephant; Randomly selecting an animal with a long tail
7. Select the procedure that does NOT result in a binomial distribution.
a) Surveying college students and asking them which hand is their dominant one
b) Surveying college students and asking them if they have a cell phone
c) Surveying college students and asking them what kind of mood they are in
d) Surveying college students and asking them if they are a freshman
8. Use the Standard Normal distribution to answer the following question.
Identify the probability corresponding to z-scores between -1.57 and 0.33.
a) .6875
b) .0582
c) .5711
d) .6293
Short Answer Section – Remember to show/justify your work where appropriate.
(The point value for each question is given after each question.)
A study of the percentage of alcohol content of nine randomly selected expensive beers yielded the
following data
5
8
8.1
8.3
8.5
8.6
8.6
9
9.5
9. What is the mean percentage of alcohol content? (2 pts)
10. Find the five number summary for the sample of percentage alcohol content. (6 pts)
11. Using the data set below, find the sample data value corresponding to P40. (4 pts)
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
5.34
5.57
5.88
12. How does the mean and the median compare in a distribution that is skewed to the right? Why?
(3 pts)
13. To assess the variation in volume (in cubic centimeters) of different manufacturer’s pre-filled
hormone injections, reproductive biologists select every 50th syringe beginning at a random
moment. 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 40 smokers shows the following frequencies for the cotinine levels of the smokers.
Serum Cotinine Level
(ng/ml)
0-99
100-199
200-299
300-399
400-499
Frequency
11
12
14
1
2
15. What is the class width? (2.5 pts)
16. If a relative frequency distribution were constructed for the cotinine levels, what would be the
relative frequency for the class with serum cotinine level of 100-199 ng/ml? (2.5 pts)
17. If a cumulative relative frequency distribution were constructed for the cotinine levels, what would
be the cumulative relative frequency for the class with serum cotinine level of less than 300 ng/ml?
(3 pts)
Use the sample data below for the following three questions. (3 pts each)
The following table summarizes the blood groups and Rh types for 100 typical people.
Group
Rh type
Positive
Negative
O
39
6
A
35
5
B
8
2
AB
4
1
18. If one person is randomly selected, find the probability of getting someone who is group O or Rh -.
19. If two different people are randomly selected, what is the probability that they are both from group
A and Rh + ?
20. If one person is randomly selected, find the probability of getting someone who is not in group AB.
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 74 inches tall and Jill is 68 inches tall. Who has the higher relative height? (Remember to
support your answer.) (4 pts)
Use the data below for the following four questions.
Three males with an X-linked genetic disorder have one child each. The random variable x is the
number of children among the three who inherit the X-linked genetic disorder.
X
0
1
2
3
P(X)
0.4219
0.4219
0.1406
0.0156
22. Explain why this is a valid probability distribution. (3 pts)
23. What is the probability that at most one child inherits the disorder? (3 pts)
24. Calculate the mean, E(X), for this distribution. (3 pts)
25. Calculate the variance, V(X), of this probability distribution. Recall V(X) = E(X 2) – [E(X )]2.
(4 pts)
Use the following information for the next three questions.
Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This
is the type of color blindness that causes problems with traffic signals.
26. If 20 men are randomly selected, find the probability that exactly 3 of them cannot distinguish
between red and green. (4 pts)
27. Find the standard deviation for the number of men out of 50 that cannot distinguish between red
and green. (4 pts)
28. Find the expected number of women out of 800 that cannot distinguish between red and green.
(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 public school seniors score higher than the average private school senior? (5 pts)
Use the following information to answer the next three questions.
Replacement times for CD players that fail are normally distributed with a mean of 7.1 years and a
standard deviation of 1.4 years.
30. What is the probability that a randomly selected CD player will have a replacement time more than
8.0 years? (4 pts)
31. If you want to provide a warranty so that only 1% of the CD players will fail before the warranty
expires, what time length should you make the warranty? (5 pts)
32. In a sample of 49 CD players, what is the probability that the sample mean replacement time will
not exceed 7.3 years? (5 pts)
33. In your own words, state the Central Limit Theorem. (5 pts)