Download Stats Review File Chapter 4 through 6 - Ms

Name: __________________________ Date: _____________
1. The experiment of tossing a coin 4 times has
A) 2 outcomes
B) 16 outcomes
C) 8 outcomes
D) 6 outcomes
2. Which of the following values cannot be the probability of an event?
A) 0.58
B) 1.31
C) 0.45
D) 1.00
Use the following to answer questions 3-4:
The following table gives the two-way classification of 500 students based on sex and whether or
not they suffer from math anxiety.
Sex
Male
Female
Suffer From Math Anxiety
Yes
No
156
84
179
81
3. If you randomly select one student from these 500 students, the probability that this
selected student suffers from math anxiety, given that he is a male is: (round your
answer to three decimal places, so 0.0857 would be 0.086)
4. If you randomly select one student from these 500 students, the probability that this
selected student is a female, given that she does not suffer from math anxiety is: (round
your answer to three decimal places, so 0.0857 would be 0.086)
5. In a group of 80 students, 22 are seniors. If you select one student randomly from this
group, the probability (rounded to three decimal places) that this student is a senior is:
6. In a group of 356 families, 272 own homes. If you select one family randomly from this
group, the probability (rounded to three decimal places) that this family owns a house is:
Page 1
7. You roll an unbalanced die 825 times, and a 3-spot is obtained 142 times. The
probability (rounded to three decimal places) of not obtaining a 3-spot for this die is
approximately:
8. A quality control staff selects 199 items from the production line of a company and
finds 21 defective items. The probability (rounded to three decimal places) that an item
manufactured by this company is not defective is:
Use the following to answer questions 9-16:
A pollster asked 1000 adults whether Republicans or Democrats have better domestic economic
policies. The following table gives the two-way classification of there opinions.
Sex
Male
Female
Republicans
209
181
Democrats
338
202
No Opinion
39
31
The pollster then randomly selected one adult from these 1,000 adults.
9. The probability that the selected adult is a male is: (round your answer to three decimal
places)
10. The probability that the selected adult says Democrats have better domestic economic
policies is: (round your answer to three decimal places)
11. The probability that the selected adult is a female given that she thinks that Republicans
have better domestic economic policies is approximately (round your answer to three
decimal places):
12. The probability that the selected adult has no opinion given that he is a male is
approximately (round your answer to three decimal places):
13. The joint probability (rounded to three decimal places) of events "Republicans" and
"Male" is:
Page 2
14. The probability (rounded to three decimal places) that a randomly selected adult from
these 1,000 adults is a female and holds the opinion that Democrats have better
domestic policies is:
15. The joint probability (rounded to three decimal places) of events "Male" and "No
Opinion" is:
16. The joint probability (rounded to three decimal places) of events "Republicans" and
"Democrats" is:
17. In a class of 38 students, 9 are math majors. The teacher selects two students at random
from this class. The probability (to three decimal places) that both of them are math
majors is:
18. The athletic department of a school has 13 full-time coaches, and 6 of them are female.
The director selects two coaches at random from this group. The probability (to three
decimal places) that neither of them is a female is:
19. The probability that a physician is a pediatrician is 0.18. The administration selects two
physicians at random. The probability (rounded to three decimal places) that none of
them is a pediatrician is:
20. The probability that an adult possesses a credit card is 0.79. A researcher selects two
adults at random. The probability (rounded to three decimal places) that the first adult
possesses a credit card and the second adult does not possess a credit card is:
21. The probability that a person is a college graduate is 0.36 and that he/she has high blood
pressure is 0.11. Assuming that these two events are independent, the probability (to
four decimal places) that a person selected at random is a college graduate or has high
blood pressure is
22. The probability that a corporation made profits in 2005 is 0.78 and the probability that a
corporation made charitable contributions in 2005 is 0.25. Assuming that these two
events are independent, the probability (rounded to 4 decimal places) that a corporation
made profits in 2005 or made charitable contributions in 2005, but not both is:
Page 3
23. The probability that an employee of a company is a male is 0.61 and the joint
probability that an employee of this company is a male and single is 0.15. The
probability (rounded to three decimal places) that a randomly selected employee of this
company is single given he is a male is:
24. The total number of outcomes for 3 rolls of a 9-sided die is:
25. A woman owns 15 blouses, 7 skirts, and 4 pairs of shoes. She will randomly select one
blouse, one skirt, and one pair of shoes to wear on a certain day. The total number of
possible outcomes is:
26. The probability that a student at a university is a male is 0.52, that a student is a business
major is 0.17, and that a student is a male and a business major is 0.07. The probability
that a randomly selected student from this university is a male or a business major is:
27. The probability that a family has at least one child is 0.76, that a family owns a
camcorder is 0.19, and that a family has at least one child and owns a camcorder is 0.08.
The probability that a randomly selected family has at least one child or owns a
camcorder is:
Use the following to answer question 28:
A consume researcher inspects 300 batteries manufactured by two companies for being good or
defective. The following table gives the two-way classification of these 300 batteries.
Company A
Company B
Good
137
133
Defective
13
17
28. If the researcher selects one battery at random from these 300 batteries, the probability
(rounded to three decimal places) that this battery is good or made by company B is
29. The probability that a person drinks at least five cups of coffee per day is 0.31, and the
probability that a person has high blood pressure is 0.09. Assuming that these two
events are independent, find the probability (to four decimal places) that a person
selected at random drinks less than five cups of coffee per day and has high blood
pressure.
Page 4
30. Friends will be called, one after another, and asked to go on a weekend trip with you.
You will call until one agrees to go (A) or four friends are asked. What is the tree
diagram for the sample space for this experiment?
A)
B)
C)
D)
Page 5
31. Pioneer Of The Nile (A), I Want Revenge (B), and Hold Me Back (C), were the three
favorites to win the Kentucky Derby. According to an expert, they should arrive first,
second and third, respectively.
The tree diagram for the sample space is given below.
A) Complete the tree diagram from top to bottom
B) State the composition of the event E = [exactly two horses arrived in the predicted
place]
32. The factorial of 9 is:
33. The factorial of (15 - 8) is:
34. The number of combinations for selecting 7 elements from 10 distinct elements is:
35. A court randomly selects a jury of 6 persons from a group of 20 persons. The total
number of combinations is:
36. The probability of rolling a 1 on a die and flipping tails on a coin at the same time is:
37. Given the table.
Male
Female
Yes
0.083
0.185
No
0.129
0.135
Maybe
0.371
0.097
What is the probability that a randomly selected Male will answer "Yes" or "No"?
Page 6
Use the following to answer questions 38-43:
The following table lists the probability distribution of a discrete random variable x:
x
P(x)
0
0.04
1
0.11
2
0.18
3
0.28
4
0.11
5
0.16
6
0.09
7
0.03
38. The probability of x  3 is:
39. The probability that x is less than 5 is:
40. The probability that x is greater than 3 is:
41. The probability that x is less than or equal to 5 is:
42. The probability that x is greater than or equal to 4 is:
43. The probability that x assumes a value from 2 to 5 is:
Use the following to answer question 44:
The following table lists the probability distribution of the number of refrigerators owned by all
families in a city.
x
P(x)
0
0.02
1
0.64
2
0.25
3
0.09
44. The probability that a randomly selected family owns at most one refrigerator is:
Page 7
Use the following to answer questions 45-46:
The following table lists the probability distribution of a discrete random variable x:
x
P(x)
0
0.04
1
0.11
2
0.18
3
0.28
4
0.11
5
0.16
6
0.09
7
0.03
45. The mean of the random variable x is:
46. The standard deviation of the random variable x, rounded to three decimal places, is:
47. Eight percent of all college graduates hired by companies stay with the same company
for more than five years. The probability, rounded to four decimal places, that in a
random sample of 12 such college graduates hired recently by companies, exactly 5 will
stay with the same company for more than five years is:
48. Thirty-two percent of adults did not visit their physicians' offices last year. The
probability, rounded to four decimal places, that in a random sample of 8 adults, exactly
2 will say they did not visit their physicians' offices last year is:
49. 57% of children in a school do not have cavities. Let x be the number of children in a
random sample of 44 children selected from this school who do not have cavities. The
mean and standard deviation of the probability distribution of x, rounded to two decimal
places, are:
Use the following to answer questions 50-52:
A manufacturer packages bolts in boxes containing 100 each. Each box of 100 bolts contains, on
average, 3 defective bolts. The quality control staff randomly selects a box at the end of the day
from an entire production run.
50. What is the probability, rounded to four decimal places, that the box will contain exactly
3 defective bolts?
51. What is the probability, rounded to four decimal places, that the box will contain at most
7 defective bolts?
Page 8
52. What is the probability, rounded to four decimal places, that the box will contain less
than 8 defective bolts?
53. A survey show that out of 1,000 households surveyed, 389 own one car, 372 own two
cars, 214 own three cars, and 25 own 4 or more cars. Construct the probability
distribution for this data.
54. For the standard normal distribution, the area between z = 0 and z = 0.79, rounded to
four decimal places, is:
55. For the standard normal distribution, the area between z = 0 and z = –2.01, rounded to
four decimal places, is:
56. For the standard normal distribution, the area to the right of z = 0.26, rounded to four
decimal places, is:
57. For the standard normal distribution, the area to the right of z = –0.91, rounded to four
decimal places, is:
58. For the standard normal distribution, the area to the left of z = 1.27, rounded to four
decimal places, is:
59. Let x have a normal distribution with a mean of 58.0 and a standard deviation of 3.19.
The z value for x = 61.83, rounded to two decimal places, is:
60. Let x have a normal distribution with a mean of 119.0 and a standard deviation of 11.84.
The z value for x = 80.56, rounded to two decimal places, is:
61. Let x have a normal distribution with a mean of 8.9 and a standard deviation of 2.67.
The z value for x = 8.55, rounded to two decimal places, is:
62. Let x have a normal distribution with a mean of –29.9 and a standard deviation of 9.89.
The z value for x = –64.52, rounded to two decimal places, is:
Page 9
Use the following to answer questions 63-65:
The GMAT scores of all examinees who took that test this year produce a distribution that is
approximately normal with a mean of 430 and a standard deviation of 49.
63. The probability that the score of a randomly selected examinee is between 400 and 480,
rounded to four decimal places, is:
64. The probability that the score of a randomly selected examinee is less than 370, rounded
to four decimal places, is:
65. The probability that the score of a randomly selected examinee is more than 530,
rounded to four decimal places, is:
Use the following to answer questions 66-68:
The net weights of all boxes of Top Taste cookies produce a distribution that is approximately
normal with a mean of 32.17 and a standard deviation of 0.69.
66. The probability that the net weight of a randomly selected box of these cookies is more
than 32.6 ounces, rounded to four decimal places, is:
67. The probability that the net weight of a randomly selected box of these cookies is less
than 31.58 ounces, rounded to four decimal places, is:
68. The probability that the net weight of a randomly selected box of these cookies is
between 31.8 and 32.5 ounces, rounded to four decimal places, is:
69. The area under the standard normal curve from zero to z is 0.4884 and z is positive. The
value of z is:
70. The area under the standard normal curve from zero to z is 0.4678 and z is negative. The
value of z is:
Page 10
71. The area under the standard normal curve to the right of z is 0.2912 and z is positive.
The value of z is:
72. The area under the standard normal curve to the left of z is 0.0409 and z is negative. The
value of z is:
Use the following to answer questions 73-75:
We know that 59% of all adults are in favor of abolishing the sales tax and increasing the income
tax. Suppose we take a random sample of 425 adults and obtain their opinions on the issue.
73. The probability that exactly 250 will be in favor of abolishing the sales tax and
increasing the income tax is approximately:
74. The probability that 225 or fewer will be in favor of abolishing the sales tax and
increasing the income tax is approximately:
75. The probability that 250 to 265 will be in favor of abolishing the sales tax and
increasing the income tax is approximately:
76. You are given that the area under the standard normal curve to the left of z = –0.99 is
equal to 0.1611. What is P(–0.99< z < 0.99)?
77. Suppose that the random variable x has a binomial distribution with n = 42 and p = 0.45.
You want to determine P 14  X  19 . Using the normal approximation, what is this
probability? (Round the answer to 4 decimal places.)
78. 94.5% of the parts coming off an assembly line are non-defective. Using the normal
approximation to the binomial distribution, what is the probability, rounded to four
decimal places, that of 488 parts, fewer than 467 are non-defective?
Page 11
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31A.
31B.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
B
B
0.650
0.491
0.275
0.764
0.828
0.894
0.586
0.540
0.464
0.067
0.209
0.202
0.039
0
0.051
0.269
0.672
0.166
0.4304
0.6400
0.246
729
420
0.62
0.87
0.957
0.0621
C
B, C, A, C, A, B
E={}
362,880
5,040
120
38,760
1/12
0.212
0.28
0.72
0.39
0.88
0.39
0.73
Page 12
44.
45.
46.
47.
48.
49A.
49B.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
0.66
3.30
1.712
0.0014
0.2835
The mean is 25.08.
The standard deviation is 3.28.
0.2240
0.9881
0.9881
Number of cars owned
Probability
1
0.389
2
0.372
3
0.214
4 or more
0.025
0.2852
0.4778
0.3974
0.8186
0.8980
1.20
–3.25
–0.13
–3.50
0.5760
0.1104
0.0206
0.2666
0.1963
0.3879
2.27
–1.85
0.55
–1.74
0.0392
0.0064
0.4762
0.6778
0.5268
0.8960
Page 13