Biometry 109, Midterm 1, Spring 2007
Name (print):_____________________
I confirm that I am allowed only a calculator and one 3-by-5 inch note card of notes for
this exam. I will not look at anybody else’s exam and I will take all necessary efforts to
prevent others from seeing my exam. I will use the provided Z-table to cover up my
work and answers. The consequence of using additional test aids, copying from others,
or allowing others to copy my work will result in disciplinary action.
I have read and agree with the above statement.
Signature: _____________________
1. 4pts. Answer:_____________. Using the values y1  2, y 2  7, y 3  6 calculate
n
 y
i 1
 y  . Show your work.
2
i
For the following blanks, fill in whether the random variable is Categorical, Continuous,
or Discrete.
2. 1pt. Answer:_____________ The number of mice in a litter.
3. 1pt.Answer:_____________ The length of a steelhead.
4. 1pt.Answer: _____________ How many students attend a Friday lecture.
5. 1pt.Answer: _____________ Blood type of a patient.
Stem-and-leaf of Center N
Leaf Unit = 1.0
2
2
88
8
3
034589
17
4
013355689
29
5
012223335589
42
6
0013345555678
(11) 7
00000113559
47
8
0033689
40
9
000124568
31
10 02222233556789
17
11 012257799
8
12 112
5
13 2577
1
14
1
15 0
= 100
6. 2pts.Answer: ______________The above stem-and-leaf plot shows the lengths of
100 ivy leaves. How many leaves were 8.3cm long?
Name:_______________
Boxplot of Change in Temperature vs Treatment
Change in Temperature
4
3
2
1
0
-1
cool
hot
Treatment
nothing
The above boxplot graph shows the increase in body temperatures of three different
groups of students at the HSU health center after receiving one of three treatments
(“cool”, “hot”, “nothing”).
7. 2pts.Answer:__________________ Which group has the greatest median
increase?
8. 2pts.Answer:__________________ Which group has the greatest range?
9. 2pts.Answer: __________________ Which group has the largest difference
between its 50th and 75th percentiles?
10. 2pts.Answer: __________________ Which group has the smallest interquartile
range?
Tally for Discrete Variables: hair
hair
black
blond
brown
lightbrown
red
N=
Count
6
31
20
8
4
69
11. 3pts.Answer:__________________The above tally is for the childhood hair color
of 69 students in a class. If you were to create a pie chart of hair colors, how
many degrees of the circle would be allocated to blond hair? Show your work.
2
Name:_______________
Suppose the female (sow) American Black Bear (Ursus americanus) has anywhere
between 1 and 4 cubs at one time. The probabilities are listed below with the exception
of some probabilities left blank. Let Y represent the number of cubs.
y pdf: P(Y=y) cdf: P(Y  y)
1 0.18
??
2
0.50
??
3
?
??
4
0.02
??
12. 4pts. Fill in the missing probability for the probability of a sow having 3 cubs.
13. 4pts. Fill in the cumulative distribution function (cdf) column.
14. 4pts. Answer:_________________Use the above table to calculate the number of
cubs a sow is expected to have. That is, calculate E (Y )   . Show your work.
15. 3pts. Circle which sentence best describes the Central Limit Theorem.
(a) If you sample many values from a population, the distribution of your sampled
values will be approximately normal.
(b) If you take many different large samples from a population, the population
will be approximately normally distributed.
(c) If you take many different large samples from a population, the distribution of
the sample means calculated from the different samples will be approximately
normally distributed.
3
Name:_______________
Let event A be defined as a person having a certain disease. Let event B be defined as a
tested person testing positive for the disease. Suppose people are tested at random.
Using the following probabilities, answer the following questions.
P( A)  0.1
P ( B | A)  0.85 (true positive)
P( B C | AC )  0.95 (true negative)
16. 1pt. The probability of a person testing negative given that they do not have the
disease, P( B C | AC )  0.95 , is known as the__________________ of the test.
17. 1pt. The probability of a person testing positive given that they do have the
disease, P( B | A)  0.85 , is known as the __________________ of the test.
18. 3pts. Answer:___________________ Calculate the probability of a random
person not having the disease; i.e., P( AC ) .
19. 3pts. Answer: __________________ Calculate the probability of a random
person having the having the disease and testing positive; i.e., P( A  B) . Show
your work.
20. 3pts. Answer: _______________ Calculate the probability of a random person
testing positive; i.e., P(B). Show your work. (Hint, a tree may help you here.)
4
Name:_______________
21. 2pts. In the above Venn Diagram, shade in the region represented by AC  B
22. 2pts. In the above Venn Diagram, shade in the region represented by A  B .
5
Name:_______________
Suppose the probability of a bear cub reaching maturity is 0.7. 9 cubs are tagged and
followed until either death or maturity. Assume independence and equal probability of
survival for each cub; i.e., think binomial distribution. Use this information to answer the
following probabilities.
23. 3pts. Answer:________________ What is the expected number of cubs, µ, that
will reach maturity. Show your work.
24. 6pts. Answer: ________________ Calculate the probability of exactly 5 out of
the 9 cubs reaching maturity; i.e., P(Y=5). Show your work.
25. 3pts. Answer: ________________ Calculate the probability of 8 or fewer cubs
reaching maturity; i.e., P(Y  8) . Show your work.
26. 6pts. Answer:_________________ Let Z be a standard normal random variable.
Use the Z-table to calculate P(1.23  Z  0.57) . Show your work.
27. 3pts. Answer:_________________ Let Z be a standard normal random variable.
Calculate the 67th percentile of the Z random variable.
6
Name:_______________
28. 5pts. Answer:_________________ Suppose the length of a certain species of
fish is normally distributed with   40 cm and   5 . Calculate the proportion
of fish less than 42 cm; i.e., P(Y  42) . Show your work including the z-score.
29. 4pts. Answer: _________________ Calculate the 67th percentile of fish lengths.
Show your work using the z-score.
30. 4pts. Answer: _________________ Suppose you were capture 25 fish at
random. Calculate the probability of the average fish length being less than
42cm; i.e., P(Y  42) . Show your work including your z-score.
7