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Palo Verde – Spring 2024
MAT 106 Statistics
Midterm Exam
I. True/False Questions (circle one) (2 points each)
True or False
1. Convenience samplings could result in having sampling biases.
True or False
2. When most of the data values fall to the right, the distribution is skewed to the right.
True or False
3. The probability of winning lottery with a ticket is 50% because you either win or lose.
True or False
4. In a binomial experiment, the trials must be dependent.
True or False
5. Exp(0.37) is an exponential distribution with decay parameter of 0.37.
True or False
6. We use z =
True or False
7. The Central Limit Theorem requires samples to be at least size 45.
x−μ
σ
to go back and forth from standard to normal distribution.
II. Multiple-choice Questions (circle one) (2 points each)
8. Which of these is an example of qualitative data?
a. test scores (i.e. 95%)
b. distances (i.e. 4 miles)
c. zip code (i.e. 92225)
9. Which of these is a measure of spread of data?
a. means
b. variances
c. quartiles
d. percentiles
e. medians
10. Which of these is a conditional probability?
a. P(A)
b. P(B|A)
c. P(A OR B)
d. P(A AND B)
11. The complement of X > 3 is
a. X ≤ 3
b. X ≥ 3
c. X = 3
d. X < 3
12. If X has a uniform distribution on the interval 5 < X < 15, then
a. X ~ U(6, 14)
b. X ~ N(5, 15)
c. X ~ U(5, 15)
d. X ~ B(5, 15)
d. time (i.e. 9am)
Palo Verde – Spring 2024
MAT 106 Statistics
13. The calculator function for finding P(X > 2.57) where X ~ N(3, 2) is
a. normalcdf(2.57, 1E99, 3, 2)
b. normalcdf(-1E99, 2.57, 3, 2)
c. invNorm(2.57, 3, 2)
d. invNorm(-2.57, 3, 2)
14. The standard deviation of the sampling distribution for sample means is
a. σ
b. μ
c. √ *σ
d. √
e.
σ
√n
III. Essay Questions
15. Sixty adults with gum disease were asked the number of times per week they used to floss before
their diagnosis. The results are shown below.
a. Fill in the blanks for the above table. (2 points)
b. What percent of adults flossed six times per week? (2 points)
c. What percent flossed at most three times per week? (2 points)
Palo Verde – Spring 2024
MAT 106 Statistics
16. The box plot below shows the ages of the U.S. population in 1990.
a.
b.
c.
d.
What is the median for this data, and how do you know? (2 points)
What are the first and third quartiles for this data, and how do you know? (4 points)
What is the interquartile range for this data? (2 points)
What is the range for this data? (2 points)
17. The following table identifies a group of children by one of four hair colors, and by type of hair.
a.
b.
c.
d.
Complete the table above. (2 points)
Find P(straight | blond). (2 points)
What is the probability that a child has wavy hair? (2 points)
Are the events “wavy” and “brown” independent? Justify your answer numerically. (4 points)
Palo Verde – Spring 2024
MAT 106 Statistics
18. In a particular community, 65 percent of households include at least one person who has graduated
from college. You randomly sample 100 households in this community. Let X = the number of
households including at least one college graduate.
a. Describe the probability distribution of X. (2 points)
b. What is the mean of X? (2 points)
c. What is the standard deviation of X? (2 points)
19. A fireworks show is designed so that the time between fireworks is between one and five seconds,
and follows a uniform distribution.
a. Find the average time between fireworks. (2 points)
b. Find the probability that the time between fireworks is greater than four seconds. (5 points)
Palo Verde – Spring 2024
MAT 106 Statistics
20. IQ is normally distributed with a mean of 125 and a standard deviation of 20. Suppose one individual
is randomly chosen. Let X = IQ of an individual.
a. Define the distribution for X. (2 points)
b. Find the probability that the person has an IQ greater than 140. Include a sketch of the graph,
and write a probability statement. (7 points)
c. MENSA is an organization whose members have the top 3% of all IQs. Find the minimum IQ
needed to qualify for the MENSA organization. Sketch the graph, and write the probability
statement. (7 points)
d. The middle 55% of IQs fall between what two values? Sketch the graph and write the probability
statement. (7 points)
Palo Verde – Spring 2024
MAT 106 Statistics
21. A manufacturer makes screws with a mean diameter of 0.15 cm and a range of 0.40 cm to 0.50 cm;
within that range, the distribution is uniform.
a. If X = the diameter of one screw, what is the distribution of X? (2 points)
b. Suppose you repeatedly draw samples of size 150 and calculate their mean. Applying the central
limit theorem, what is the distribution of these sample means? (4 points)
c. Suppose you repeatedly draw samples of size 80 and calculate their sum. Applying the central
limit theorem, what is the distribution of these sample sums? (4 points)
IV. Bonus Questions
22. In a recent study, the mean age of tablet users is 34 years. Suppose the standard deviation is 15
years. Take a sample of size n = 100.
a.
b.
c.
d.
What are the mean and standard deviation for the sample mean ages of tablet users? (2 points)
What does the distribution look like? (1 point)
Find the probability that the sample mean age is more than 30 years. (1 point)
Find the 95th percentile for the sample mean age. (1 point)
Palo Verde – Spring 2024
MAT 106 Statistics
23. Suppose X has a normal distribution with mean 25 and standard deviation 5. Between what values of
X do 68% of the values lie? (Sketch the graph and write a probability statement, 5 points)
24. The university library records the number of books checked out by each patron over the course of
one day, with the following result:
a. What is P(x > 2)? (2 points)
b. What is the average number of books taken out by a patron? (3 points)
25.
a. Events A and B are independent. If P(A) = 0.3 and P(B) = 0.5, find P(A AND B). (3 points)
b. C and D are mutually exclusive events. If P(C) = 0.18 and P(D) = 0.03, find P(C OR D). (2 points)
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