78)
f(x) =x
3–1
6; [3, 4]
78)
A)
0.24
B)
0.32
C)
0.28
D)
0.25
Find a value of k that will make f a probability density function on the indicated interval.
79)
f(x) = kx2; [1, 3]
79)
A)
3
28
B)
3
26
C)
1
13
D)
1
9
Find the proportion of observations of a standard normal distribution that are between the given z–scores.
80)
–1.2 and 0.5
80)
A)
0.1934
B)
0.5601
C)
0.5784
D)
0.5764
Find the probability to the nearest hundredth that the random variable of the probability density function has a value
greater than the mean.
81)
f(x) =x
8–1
4; [2, 6]
81)
A)
0.55
B)
0.46
C)
0.54
D)
0.50
Find the cumulative distribution function for the given probability density function.
82)
f(x) =3
56 x2; [2, 4]
82)
A)
F(x) =x3– 2
56 , 2 x
4
B)
F(x) =x3+ 8
56 , 2 x
4
C)
F(x) =x3– 8
56 , 2 x
4
D)
F(x) =x3
56 , 2 x
4
Solve the problem.
83)
The time between major earthquakes in the Alaska panhandle region is a random variable with
probability density function f(x) =1
640e–x/640 for x in [0, ), where t is measured in days. Find the
probability that the time between a major earthquake and the next one is less than 200 days.
83)
A)
0.7316
B)
0.0004
C)
0.2684
D)
0.0011
Find the expected value of the probability density function to the nearest hundredth.
84)
f(x) = 2(1 – x); [0, 1]
84)
A)
0.67
B)
1.00
C)
0.50
D)
0.33
Solve the problem.
85)
The life span of a certain insect in days is uniformly distributed over the interval [20, 36]. What is
the expected life of this insect?
85)
A)
29 days
B)
30 days
C)
28 days
D)
26 days
Find the mean and standard deviation of the specified probability density function.
86)
f(x) = 0.6e–0.6x for [0, )
86)
A)
µ= 1.71, = 1.67
B)
µ= 1.67, = 1.67
C)
µ= 16.67, = 16.67
D)
µ= 1.5, = 1.5
Solve the problem.
87)
The time of a telephone call (in minutes) to a certain town is a continuous random variable with a
probability density function defined by f(x) =4x–5 for x 1. Find the probability that the call lasts
between 1 and 2 minutes.
87)
A)
0.8125
B)
1.0625
C)
0.0625
D)
0.9375
Find the probability to the nearest hundredth that the random variable of the probability density function has a value
greater than the mean.
88)
f(x) =1
5; [0, 5]
88)
A)
0.53
B)
0.50
C)
0.45
D)
0.49
Solve the problem.
89)
The annual rainfall in Maine is a random variable with probability density function defined by
f(x) =1
15 x +1
2 for x in [0, 5]. Find the probability of rainfall greater than one standard deviation
above the mean.
89)
A)
0.159
B)
0.086
C)
0.188
D)
0.346
Find the expected value of the probability density function to the nearest hundredth.
90)
f(x) = 3x–4; [1, )
90)
A)
1.25
B)
1.75
C)
1.00
D)
1.50
91)
f(x) =1
5; [0, 5]
91)
A)
5.00
B)
2.40
C)
2.50
D)
12.50
92)
f(x) = 4x–5; [1, )
92)
A)
1.00
B)
0.80
C)
1.67
D)
1.33
Find the probability to the nearest hundredth that the random variable of the probability density function has a value
greater than the mean.
93)
f(x) =3x2
98 ; [3, 5]
93)
A)
0.62
B)
0.50
C)
0.56
D)
0.54
Find the variance of the probability density function to the nearest hundredth.
94)
f(x) = 3x–4; [1, )
94)
A)
0.69
B)
0.73
C)
0.50
D)
0.75
Decide whether or not the function is a probability density function on the indicated interval.
95)
f(x) =2
109x2–2
109x +1
654; [0, 6]
95)
A)
Yes
B)
No
Find the mean and standard deviation of the specified probability density function.
96)
f(x) =1
7 for [6, 13]
96)
A)
µ= 3.45, = 2.02
B)
µ= 3.50, = 2.02
C)
µ= 9.50, = 1.73
D)
µ= 9.50, = 2.02
Find a value of k that will make f a probability density function on the indicated interval.
97)
f(x) = kx2; [0, 3]
97)
A)
1
9
B)
1
27
C)
3
26
D)
2
9
Solve the problem.
98)
A machine produces bolts with an average diameter of 0.30 inches and a standard deviation of 0.01
inches. What is the probability that a bolt will have a diameter greater than 0.32 inches? Assume
the distribution is normal.
98)
A)
2%
B)
3%
C)
1%
D)
98%
Find the proportion of observations of a standard normal distribution that are between the given z–scores.
99)
1.26 and 2.15
99)
A)
0.0862
B)
0.0898
C)
0.0881
D)
0.5880
Use the standard normal curve table to find the z–score for the given condition.
100)
33% of the total area is to the right of z.
100)
A)
0.74
B)
0.44
C)
–0.44
D)
0.45
101)
82.89% of the total area is to the left of z.
101)
A)
0.95
B)
0.96
C)
–0.96
D)
–0.95
Find the standard deviation of the probability density function to the nearest hundredth.
102)
f(x) =1
3; [3, 6]
102)
A)
0.61
B)
0.86
C)
0.94
D)
0.87
Solve the problem.
103)
The annual rainfall in Maine is a random variable with probability density function defined by
f(x) =1
15 x +1
2 for x in [0, 5]. Find the variance.
103)
A)
0.815
B)
1.601
C)
1.643
D)
2.550
Use the standard normal curve table to find the z–score for the given condition.
104)
25.14% of the total area is to the right of z.
104)
A)
0.67
B)
–0.68
C)
0.33
D)
–0.67
Find the mean and standard deviation of the specified probability density function.
105)
f(x) = 5 for [5.2, 5.4]
105)
A)
µ= 5.32, = 0.058
B)
µ= 5.30, = 0.058
C)
µ= 5.30, = 0.056
D)
µ= 5.39, = 0.056
Find the expected value of the probability density function to the nearest hundredth.
106)
f(x) = 1 –1
x; [1, 4]
106)
A)
2.50
B)
2.83
C)
3.00
D)
2.67
Solve the problem.
107)
The life span of a certain insect in days is uniformly distributed over the interval [20, 36]. What is
the probability the insect will live 24 days or less?
107)
A)
0.25
B)
0.75
C)
0.20
D)
0.24
Find the probability to the nearest hundredth that the value of the random variable is within one standard deviation of
the mean.
108)
f(x) =1
2x; [0, 2]
108)
A)
0.75
B)
0.63
C)
0.69
D)
0.50
Find the standard deviation of the probability density function to the nearest hundredth.
109)
f(x) =1
6; [2, 8]
109)
A)
1.73
B)
1.66
C)
1.72
D)
1.69
Solve the problem.
110)
The time of a telephone call (in minutes) to a certain town is a continuous random variable with a
probability density function defined by f(x) =5x–6 for x 1. Find the probability that the call lasts
more than 2 minutes.
110)
A)
0.9688
B)
0.0625
C)
0.0313
D)
0.8438
Find the variance of the probability density function to the nearest hundredth.
111)
f(x) =x
3–1
6; [3, 4]
111)
A)
0.05
B)
0.08
C)
0.10
D)
0.06
Solve the problem.
112)
The annual rainfall in Maine is a random variable with probability density function defined by
f(x) =1
15 x +1
2 for x in [0, 5]. Find the probability of rainfall within one standard deviation from
the mean.
112)
A)
0.594
B)
0.365
C)
0.622
D)
0.612
Find the variance of the probability density function to the nearest hundredth.
113)
f(x) = 2(1 – x); [0, 1]
113)
A)
0.06
B)
0.60
C)
1.50
D)
1.00
Find a value of k that will make f a probability density function on the indicated interval.
114)
f(x) = kx2; [1, 2]
114)
A)
3
7
B)
1
2
C)
3
8
D)
1
3
Find the variance of the probability density function to the nearest hundredth.
115)
f(x) =3x2
98 ; [3, 5]
115)
A)
0.33
B)
0.31
C)
0.25
D)
0.27
116)
f(x) =x
8–1
4; [2, 6]
116)
A)
0.84
B)
0.16
C)
0.91
D)
0.88
Solve the problem.
117)
The life span of a certain insect in days is uniformly distributed over the interval [20, 36]. What is
the probability an insect will live between the mean and one standard deviation above the mean?
117)
A)
0.28
B)
0.25
C)
0.79
D)
0.29
118)
The annual rainfall in Maine is a random variable with probability density function defined by
f(x) =1
15 x +1
2 for x in [0, 5]. Find the probability that the rainfall is less than the mean.
118)
A)
0.447
B)
0.500
C)
0.489
D)
0.445
Use the standard normal curve table to find the z–score for the given condition.
119)
4.01% of the total area is to the left of z.
119)
A)
1.70
B)
–1.75
C)
–1.76
D)
–1.74
Find the probability to the nearest hundredth that the random variable of the probability density function has a value
greater than the mean.
120)
f(x) = 1 –1
x; [1, 4]
120)
A)
0.50
B)
0.48
C)
0.55
D)
0.53
Solve the problem.
121)
The life (in months) of an automobile battery has a probability density function defined by
f(x) =1
4e–x/4 for x in [0, ). Find the probability that the life of a randomly selected battery is
greater than 7 years.
121)
A)
0.0434
B)
0.1738
C)
0.8262
D)
0.2066
Find the mean and standard deviation of the specified probability density function.
122)
f(x) =1
8 for [12, 20]
122)
A)
µ= 1.6, = 2.29
B)
µ= 15, = 2.31
C)
µ= 15.5, = 2.28
D)
µ= 16, = 2.31
Find the standard deviation of the probability density function to the nearest hundredth.
123)
f(x) =3x2
98 ; [3, 5]
123)
A)
0.54
B)
0.50
C)
0.61
D)
0.56
Find the variance of the probability density function to the nearest hundredth.
124)
f(x) =1
6; [2, 8]
124)
A)
2.86
B)
2.98
C)
2.75
D)
3.00
Find a value of k that will make f a probability density function on the indicated interval.
125)
f(x) = kx3; [1, 2]
125)
A)
1
4
B)
3
16
C)
4
15
D)
4
17
Use the standard normal curve table to find the z–score for the given condition.
126)
74.86% of the total area is to the left of z.
126)
A)
–0.67
B)
0.68
C)
0.66
D)
0.67
Find the expected value of the probability density function to the nearest hundredth.
127)
f(x) =x
3–1
6; [3, 4]
127)
A)
3.75
B)
3.50
C)
8.28
D)
3.53
Find the variance of the probability density function to the nearest hundredth.
128)
f(x) =1
3; [3, 6]
128)
A)
0
B)
0.38
C)
0.75
D)
1.89
Find a value of k that will make f a probability density function on the indicated interval.
129)
f(x) = kx1/2; [1, 9]
129)
A)
1
56
B)
3
54
C)
3
17
D)
3
52
Use the standard normal curve table to find the z–score for the given condition.
130)
30.15% of the total area is to the right of z.
130)
A)
0.53
B)
–0.52
C)
0.88
D)
0.52
Answer Key
Testname: C11
Answer Key
Testname: C11
Answer Key
Testname: C11