STAT 111 --- Midterm Name:
October 23, 2001 Student ID #:
This is a closed book exam; you may use a calculator. You can use a sheet with the formulas you may need. Show your work to receive full credit. All questions carry the same points (4 pts). The needed tables are provided.
1.
A group of researchers want to ensure that they have a representative sample of the population being studied. To do this, they assign a number to every member of the population and then use a randomly generated number to choose the subjects to be included in their sample. What type of sample is this? a.
measurement b.
biased c.
random d.
population subset
2. The sex of a baby is an example of ____________ data; the height and weight of
the baby are examples of ___________ data. a.
qualitative; quantitative b.
descriptive; inferential c.
qualitative; inferential d.
descriptive; quantitative
3.
When a researcher is analyzing data, he/she will usually want to quantify the spread or
_______________ of the data. a.
variability b.
mode c.
central tendency d.
mean
4. Given the following data, find the median of the data set: 3 3 1 5 13 12 12 9 6 a.
3 b.
6 c.
9 d.
12

5. Given the following data, find the mode of the data set: 3 3 1 5 13 12 12 9 6 a.
13 b.
3 c.
12 d.
none of the above
6. Calculate the mean for the following data.
3 9 8 5 7 9 4 6 5 5 4 6 8 4 5 0 a.
5.5 b.
4.0 c.
7.25 d.
5
7. Calculate the standard deviation for the following data.
3 9 8 5 7 9 4 6 5 5 4 6 8 4 5 0 a.
7.25 b.
5.6 c.
3.53 d.
2.37
8. Find the sample z score of the value 3 for the data of exercises 6 and 7 a.
–0.45 b.
1.06 c.
–1.06 d.
3
9. Describe how the mean compares to the median for a distribution skewed to the left: a.
it is larger b.
it is smaller c.
they are the same
10. The data set of A

B would consist of a.
the sample points belonging to neither A or B. b.
all the sample points belonging to both A and B. c.
the complement of A and B. d.
all the sample points belonging to either A or B or both.

11. The data set of A

B consists of a.
the sample points belonging to neither A or B. b.
all the sample points belonging to both A and B. c.
the complement of A and B. d.
all the sample points belonging to either A or B or both.
12. A professor grades his exams on a steep curve. He expects to see the following grades in his class: A (5%), B (10%), C (50%), D (10%), and F(?%). From these possible grades, what percentage of the class is expected to fail the course? a.
50% b.
25% c.
5% d.
10%
13. Given below are the data for two popular activities. Relative age groups have been recorded for people who practice these sports regularly. Event A consists of the percentage of people who plan to go hiking during the summer, and event B is defined as people between the ages of 20 and
30 who either mountain bike or hike.
Hiking Mountain biking Age
< 20
20-30
>30
0.18
0.21
0.34
0.05
0.13
0.09
Calculate the probability for the union of events A and B . a.
0.86 b.
1.00 c.
0.73 d.
0.21
14. Calculate the probability for the intersection of events A and B in question 13 above. a.
0.86 b.
0.73 c.
0.21 d.
0.13
15.
The next president will be either a Republican, a Democrat, or from the Independent party.
The three parties are examples of a.
independent events

b.
mutually exclusive events c.
a union of two events d.
complementary events
16. The probability of event A occurring is 0.75. Given that event A has occurred, then the
probability of event B occurring is 0.43. Calculate the probability of the intersection of events
A and B. a.
0.32 b.
0.75 c.
0.21 d.
0.43
17. Suppose P(A)=.7 and P(B)=.5. The statement “events A and B are mutually exclusive” is: a.
true b.
false c.
do not have enough information to answer
18. Suppose an urn contains 3 black marbles and 4 white marbles. Suppose you randomly draw
two marbles without replacement. What is the probability you get two marbles of different
color? a. 2/7 b. 4/7 c. 12/49 d. 6/42
19. Suppose a bookie will give you $5 for every $1 you risk if you pick the winners in three
ballgames. Thus, for every $1 you bet you will either lose $1 or gain $4. What is the bookie’s
expected earnings per dollar wagered? a. –$3/8 b. $11/8 c. $3/8 d. $21/27
20. What is the difference between Chebyshev's Rule and the Empirical Rule? a.
Chebyshev's Rule applies to any probability distribution; the Empirical Rule applies only to distributions when 95% of the data points fall within one standard deviation of the mean. b.
Chebyshev's Rule applies only to distributions when 68% of the data points fall within one standard deviation of the mean; the Empirical Rule applies only to mound or symmetrical distributions.

c.
Chebyshev's Rule applies to any probability distribution; the Empirical Rule applies only to distributions when 95% of the data points fall within two standard deviations of the mean. d.
Chebyshev's Rule applies to any mound-shaped probability distribution; the Empirical
Rule applies only to distributions when 95% of the data points fall within two standard deviations of the mean.
21. Calculate the probability that at least one out of ten products will be defective if the probability of having a defective product is 0.1. a.
0.02 b.
1.00 c.
0.65 d.
0.35
22. A coating machine coats film between 120 and 210 microns with a uniform random distribution. If any section of film with a coating greater than 200 microns cannot be sold, approximately how much of the product must be scrapped?
23. Use the standard normal table to calculate the probability that the standard normal variable z falls between 0 and 1.07. e.
0.2123 f.
0.2611 g.
0.3577 h.
0.3485 a.
1/3 b.
1/7 c.
1/2 d.
1/9
24. Find the value of the standard normal random variable z
0
such that P(-1<z<z
0
)=.5328 a. 1 b. 0.085 c. 0.5 d. –0.5

25. The random variable x has a normal distribution with standard deviation 5. It is known that
the probability that x exceeds 30 is .95. Find the mean

of the probability distribution. a.
–1.645 b.
36.4 c.
38.23 d.
21.78
EXTRA CREDIT: The birthday problem : Compute the probability that n people will have different birthdays. Assume that the year has 365 days.