Final Exam Practice Problems
1. Carbon dioxide baited traps are typically used by entomologists to monitor populations. An article in the
Journal of the American Mosquito Control Association investigated whether temperature influences the
number of mosquitoes caught in a trap. Six mosquito samples were collected on each of nine consecutive
days. For each day two variables were measured: average temperature (degrees Centigrade) and mosquito
catch ratio (the number of mosquitoes caught in each sample divided by the largest sample caught).
Average
Catch
a. Find the least squares regression line using Excel or your calculator.
Temperature Ratio
16.8
.66
15
.30
16.5
.46
17.7
.44
20.6
.67
22.6
.99
23.3
.75
18.2
.24
18.6
.51
b. What fraction of the variation of the catch ratio can be explained by the least
squares regression line using the average temperature? Use Excel or your
calculator to find the required value.
c. If the average temperature is 18°C what is the predicted catch ratio?
1d. The biologist use the regression line to predict catch ratios. Use this scenario to
explain what is meant by extrapolation.
1e. Find the corresponding residual values for the temperatures 15°C and 18.6°C.
2. A 95% confidence interval about a sample mean indicates the probability of the procedure used to create the
interval of actually containing the population mean.
a. Two individuals both take a SRS from the same population, both working independently from each other.
What is the probability that both 95% confidence intervals contain the population mean μ?
b. Eight individuals take SRS from the same population, all working independently from each other. What is the
probability that 6 of the eight 95% confidence intervals contain the population mean?
3. It is believed that adult human heights follow an approximately normal distribution. Suppose that the mean of
this distribution is 68 inches with a standard deviation of 5 inches.
a. Tim Duncan the basketball player for the San Antonio Spurs is 7 feet tall. Approximately what percentage of
people are taller than 7 feet tall?
b. If we randomly chose 4 people from the population what is the probability that average height is less than 72
inches?
4. You are given that P(A) = .34, P(B) = .45, and P(A or B) = 0.68. Do not assume that events A and B are
independent.
a. Calculate P(A and B).
b. Are events A and event B independent? You must show evidence for your conclusion in order to receive
credit.
c. P(A| B) =
5. A recent study on 12th grade students revealed information about smoking among the age group. The study
was a result of recent law suits made against CAMEL for allegedly targeting ads to minors.
Let event A be a 12th grade student smokes.
Let event B be a 12th grade student owns merchandise promoting cigarette brand names.
The study generated the following tree diagram.
a. What is the probability that a 12th grade student owns
merchandise promoting cigarette brand names, and the student
is a smoker?
b. Given that the student does not own merchandise promoting cigarettes, what is the probability that a student
smokes?
c. Suppose a student is a smoker, what is the probability that they own merchandising promoting cigarette brand
names?
6. A study in erosion produced the following data on the rate (in liters per second) at which water flows across a
soil test bed and the weight (in kilograms) of soil washed away. The r2 value for the scatter plot is 0.9395.
Interpret the meaning of this number in terms of the flow rate and eroded soil
Flow rate
0.31
(response variable)Eroded soil
0.82
0.85
1.95
1.26
2.18
2.47
3.01
3.75
6.07
7. True or False – The average, x , of a simple random sample of 20 values has more bias than an average from a
simple random sample of 100 values.
8. True or False – A sample with high bias will always have high variability.
Survival
9. Below is a graph depicting a classification of the people on the Titanic, and also the count on who survived
the accident. Answer the following questions based on the graph below.
a.
b.
c.
d.
e.
First
Second
Alive
202
118
Dead
Total
123
325
167
285
PassengerClass
Third
Crew
Total
178
212
710
528
706
673
885
1491
2201
What is the probability that someone survived the accident?
What is the probability that a first class passenger survived the accident?
If you were a first class passenger what is your chance of surviving the accident?
Given you were a third class passenger what is the probability you survived?
Is the event, “a person is alive” and the event “ a person is a first class passenger” independent?
10. True or False - The random variable X is uniformly distributed. A random sample of three values is
collected. The average is calculated for the sample. Now the distribution of averages for this situation (sampling
distribution of the mean) will be approximately normal.
11. A person is paid once a month for working at a company. Suppose that the person gets paid randomly
according to the table shown, where the random variable M is the amount of the monthly paycheck.
M
P(M)
$3124
0.5
$3560
0.3
$3900
0.15
$4100
0.05
a. What is the probability that out of 20 paychecks 13 or more are $3124?
b. What is the probility that a paycheck is more than $3124?
12. A 90% confidence interval is created to estimate ; (45, 55). The 90% means that
a. 90% of our data is between 45 and 55.
b. the probability that x will be in the interval (45, 55).
c. 90% of the time  will be between 45 and 55.
d. 90% of the time any interval we create contains .
13. Let the random variable X be uniformly distributed; x = 12.0, x = 4.2
a. What is the probability that a value is less than 8?
b. What is the probability that four values chosen at random are less
than eight.
c. What is the probability that the average of 25 values chosen at
random is less than 10?
4
20 X
0