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Stats 244.3(01) Test 2
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Solutions
I In a large Canadian City it was believed that the Pollution Index (Y) was affected by
the daily temperature (X). In order to investigate this possibility the 12 days were
selected at random from the year and on these days the daily temperature high (X) was
measured (in C). The data is tabulated below:
day
1
2
3
4
5
6
7
8
9
10
11
12
temperature high, x
Pollution index, y
24.6
102.2
9.7
41.2
19.6
86.9
3.3
19.6
14.5
63.9
16.5
69.9
6
31.6
13.9
56.7
23.3
95.7
11.6
47.9
16.4
74.5
16.7
75
Also tabled are the following important statistics
n

y
 x2
 y2
12
176.1
765.1
3031.31
55888.87
 xy
12999.06
1. Determine the value of Sxx. b
2. Determine the value of Syy. i
3. Determine the value of Sxy. d
Choices for 1, 2, 3.
a) -2663.67
f) 2349.9
b) 447.04
h) 2964.14
c) 1018.55
h) 3667.56
d) 1771.22
i) 7107.37
e) 2260.39
j) 7460.99
4. Determine the value of Pearson's r. j
5. Determine the value of Spearman's .. i
6. Determine the coefficient of determination. h
Choices for 4, 5, 6.
a) 0.7629
f) 0.9313
b) 0.7636
h) 0.9442
c) 0.8315
h) 0.9874
d) 0.854
i) 0.993
e) 0.9308
j) 0.9937
7. Determine the slope, b, of the least squares line. c
8. Determine the intercept, a, of the least squares line. f
Choices for 7, 8.
a) 1.08
f) 5.61
b) 2.5
h) 7.6
c) 3.96
h) 9.22
d) 4.16
i) 9.68
e) 4.59
j) 9.9
9.
Predict the Pollution Index (Y) when the daily temperature (X) is 15.3. f
10. Predict the Pollution Index (Y) when the daily temperature (X) is 5.0. b
Choices for 9, 10.
a) 21.45
f) 66.23
b) 25.43
h) 68.81
c) 43.2
h) 74.06
d) 46.64
i) 75.5
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e) 47.86
j) 78.5
Stats 244.3(01) Test 2
Solutions
II Based on her past experience, a doctor knows that the probability distribution for X =
number of patients who come to her office hours on Wednesday is given below.
x
0
1
2
3
4
p(x)=P(X = x)
.10
.20
.50
.15
.05
11. What is the probability that at least 2 patients come to office hours on Wednesday?
A .50
B .70
C .80
D .90
12. What is the at most 2 patients come to office hours on Wednesday, i.e. P(X
A .50
B.70
C .80
D .90
 2)?
13. What is the probability that at least 1 patient comes to office hours on Wednesday?
A .50
B.70
C .80
D .90
III A bank manager has noticed that the probability distribution for X = number of persons in line to use the
ATM machine when he leaves his office at night is shown below.
x
p(x)=P(X = x)
0
.10
1
.10
2
.40
14. What is the mean of mean of X?
A 2.0
B 2.2
C 2.5
3
.30
4
.10
D 3.0
15. The probability that there will be no more than 1 individual in line when he leaves his office at night is
A 0.10
B 0.20
C 0.70
D 0.90
16. What is the variance of X?
A . 1.08
B. 1.16
C 1.35
D 2.20
17. What is the standard deviation of X ?
A . 1.08
B. 1.16
C 1.35
D 2.20
IV: Suppose that a student needs to buy 6 books for her history course. The number of books that she will
be able to find used is a binomial random variable X with n = 6 and p = .30. In other words, the probability
that she will find any given book used is .30, and is independent from one book to the next.
18. What is the probability that she will find exactly 2 used books?
A 0.060
B. 0.185
C 0.324
D 0.600
19. What is the probability that she will find exactly 3 used books?
A . 0.060
B. 0.185
C 0.324
D 0.900
20. What is the mean number of used books she will find?
A 1.8
B. 2.0
C 3.0
D 6.0
21. What is the variance for the number of used books she will find?
A 0.54
B. 1.12
C 1.26
D 61.80
V: Find the requested probability for the standard normal random variable Z.
22. What is the probability that Z is less than or equal to 2, P(Z  2)?
A 0.0228
B. 0.2000
C 0.5000
D 0.9772
23. What is the probability that Z is greater than 2, P(Z > 2)?
A 0.0228
B. 0.2000
C 0.5000
D 0.9772
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Stats 244.3(01) Test 2
Solutions
24. What is the probability that Z is between 1 and 1, P(1  Z  1)?
A 0.1587 B. 0.3174
C 0.6826
D 0.8413
25. What is the probability that Z is between 1.2 and 1.45, P(1.2  Z  1.45)?
A 0.0303 B. 0.7740
C 0.8041
D 0.8114
V: The time taken to complete an exam, X, follows a normal probability distribution with
mean = 60 minutes and standard deviation 30 minutes.
26. What is the probability that a randomly chosen student will complete the exam in 30
minutes or less?
A 0.1587 B. 0.5000
C 0.8413
D 0.9772
27. What is the probability that a randomly chosen student will take at least an hour to
complete the exam?
A 0.1587 B. 0.5000
C 0.8413
D 0.9772
28. By what time should 67% of the students have finished the exam?
A 60.0 minutes B. 73.2 minutes C 77.9 minutes D 82.5 minutes
29. By what time should 99% of the students have finished the exam?
A 85.2 minutes B. 89.4 minutes C 129.9 minutes D 150.0 minutes
VI
30. The number of first-year students who will decide to live in dormitories is a binomial
random variable X with n = 1000 and p = 0.50. Use the normal approximation with
continuity correction to approximate the probability that X will be no more than 490,
P(X  490).
A. .2743
B. .2709
C. .7291
D. .7357
The End
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Stats 244.3(01) Test 2
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b
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