B)
= 0.20.QSCI381: Introduction to Probability and Statistics
FIRST MIDTERM Practice test
Show all work. It is not necessary that you must give final numerical answer to each problem. However, the expression which will yield the final numerical answer must be given.
#1. A sample of 7 salmon from the Puget Sound yielded the following lengths in centimeters.:
23, 25, 32, 35, 29, 40, & 26.
Which of the following statements are descriptive and which are inferential.
a) The average length of the seven salmon is 30 cm.
b) The average length of salmon in Puget Sound is 30 cm.
c) About 80% of salmon in the Sound are between 25 & 35 cm.
d) If another sample of 7 salmon are caught their length too will be between 23 & 40 cm.
[14] #2. The following is the data the frequency distribution of the number of diseased plants per bed in 150 nursery beds:
|
Diseased plants |
Frequency |
||
|
X |
f |
f*X |
f*X2 |
|
0 |
19 |
0 |
0 |
|
1 |
28 |
28 |
28 |
|
2 |
45 |
90 |
180 |
|
3 |
30 |
90 |
270 |
|
4 |
15 |
60 |
240 |
|
5 |
8 |
40 |
200 |
|
6 |
4 |
24 |
144 |
|
7 |
1 |
7 |
49 |
|
Total |
150 |
339 |
1111 |
a) Compute the mean, and standard deviation of the number of diseased plants/bed.
b) What is the median value?
c) On how many beds the number of diseased plants were more than 2, but not more than 4 per week?
d) What is the relative frequency of 3 diseased plants/bed?
#3. Jack, Jill, Adam and Evelyn have the probabilities of 0.4, 0.5, 0.6 and 0.8 respectively of hitting the target. Assuming independence in their hitting success, compute the probabilities of:
a) Jack and Jill hitting the target when only these two fire once.
b) No hits when all four fire once.
c) Only one hit when only Jack, Evelyn and Jill fire once.
#4. A forest area study resulted in the following distribution of trees:
|
Conifers |
Broad-leaved |
Total |
|
|
Healthy |
92 |
128 |
220 |
|
Diseased |
18 |
62 |
90 |
|
Total |
110 |
190 |
290 |
i. Give percentage of the trees which are broad-leaved and diseased.
ii. Give the probability that a randomly selected tree is diseased given it is a conifer.
iii. Are tree species and susceptibility to disease independent? Explain your answer using probabilities.
#5. a) Suppose that P(A) = 0.30, P(B) = 0.25, and P(AB)
= 0.20.
i. Are the events A and B independent? Explain.
ii. Find P(B|A) and P(A|B)
b) If P(A|B) = P(A) = 0.6, are events A and B mutually exclusive? Why?
c) If P(A|B) 0.6, and P(A
B)
= 0.30, what is P(B)?