Let X be a continuous random variable on a
x b with probability density function f(x). Then the median of the x–values
is that number m for which
m
a
f(x) dx =1
2.
Find the median.
81)
f(x) =1
6; 3 x 9
81)
A)
6
B)
15
2
C)
5
D)
3
Use the Poisson Distribution to find the indicated probability.
82)
In one town, the number of burglaries in a week has a Poisson distribution with =4.7. Find the
probability that in a randomly selected week the number of burglaries is at least three.
82)
A)
0.8426
B)
0.1574
C)
0.1523
D)
0.6903
E)
0.8477
83)
If the random variable x has a Poisson Distribution =0.460, find p2.
83)
A)
0.00557
B)
0.06679
C)
0.16760
D)
0.08349
Let X be a continuous random variable A
X
B and let f (x) be its probability density function and F (x) its cumulative
distribution function. Indicate whether the following statements are true or false.
84)
f(A) = 0, f(B) = 1
84)
A)
True
B)
False
85)
A random variable has probability density function f(x) = 30x2(1 – x)2(0 x 1). Compute its
cumulative distribution F(x).
85)
A)
30x2– 60x3+30x4
B)
10x3–15x4+ 6x5+ 1
C)
10x3– 15x4+ 6x5
D)
30x(1 – x)
E)
none of these
Use the Poisson Distribution to find the indicated probability.
86)
The number of calls a mountain search and rescue team receives per day has a Poisson distribution
with =0.80. Find the probability that on a randomly selected day, they will receive fewer than
two calls.
86)
A)
0.1438
B)
0.3595
C)
0.1912
D)
0.8088
Let X be a continuous random variable A
X
B and let f (x) be its probability density function and F (x) its cumulative
distribution function. Indicate whether the following statements are true or false.
87)
Pr(A X b) = F(b)
87)
A)
True
B)
False
Use the Poisson Distribution to find the indicated probability.
88)
The number of lightning strikes in a year at the top of a particular mountain has a Poisson
distribution with =3.7. Find the probability that in a randomly selected year, the number of
lightning strikes is 0.
88)
A)
0.0321
B)
0.0420
C)
0.0247
D)
0.0124
Determine whether the function is a probability density function over the given interval.
89)
f(x) =3
31 x2, 4 x 7
89)
A)
No
B)
Yes
90)
f(x) =1
2, 7 x 10
90)
A)
Yes
B)
No
Provide an appropriate response.
91)
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the
amount of beer poured by this filling machine follows a normal distribution with a mean of
12.44 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains
fewer than 12.34 ounces of beer.
91)
A)
0.9938
B)
0.4938
C)
0.5062
D)
0.0062
92)
Find the value of k that makes f(x) = kx a probability function on the interval 1 x 2.
92)
A)
6
5
B)
2
5
C)
2
3
D)
4
5
E)
none of these
Determine whether the function is a probability density function over the given interval.
93)
f(x) =1
3x, 3 x 8
93)
A)
Yes
B)
No
94)
f(x) =1
3, 6 x 9
94)
A)
Yes
B)
No
Determine the area under the standard normal curve that lies between:
95)
z =0.5 and z = 1.4
95)
A)
0.3085
B)
0.9192
C)
0.2277
D)
0.6915
96)
z = – 2 and z = – 0.4
96)
A)
0.6554
B)
0.0228
C)
0.3218
D)
0.3446
Provide an appropriate response.
97)
The length of time it takes college students to find a parking spot in the library parking lot follows a
normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the
probability that a randomly selected college student will find a parking spot in the library parking
lot in less than 4.0 minutes.
97)
A)
0.3551
B)
0.3085
C)
0.2674
D)
0.1915
98)
The length of time it takes college students to find a parking spot in the library parking lot follows a
normal distribution with a mean of 4.0 minutes and a standard deviation of 1 minute. Find the
probability that a randomly selected college student will take between 2.5 and 5.0 minutes to find a
parking spot in the library lot.
98)
A)
0.4938
B)
0.7745
C)
0.0919
D)
0.2255
Use the Poisson Distribution to find the indicated probability.
99)
A naturalist leads whale watch trips every morning in March. The number of whales seen has a
Poisson distribution with =3.4. Find the probability that on a randomly selected trip, the number
of whales seen is 5.
99)
A)
0.2148
B)
0.1264
C)
3.0327
D)
0.6318
100)
Find the expected value of the random variable whose density function is f(x) =3
8x2, 0 x 2.
100)
A)
3
2
B)
5
8
C)
5
2
D)
3
8
E)
none of these
Determine the area under the standard normal curve that lies between:
101)
z = 1 and z =3
101)
A)
0.1574
B)
0.0004
C)
0.8426
D)
0.0007
For the given probability density function, over the stated interval, find the requested value.
102)
f(x) =1
7x, over the interval 1 x 3. Find E(x).
102)
A)
26
21
B)
5
14
C)
25
21
D)
9
7
Let X be a continuous random variable A
X
B and let f (x) be its probability density function and F (x) its cumulative
distribution function. Indicate whether the following statements are true or false.
103)
B
A
F(x) = 1
103)
A)
True
B)
False
For the given probability density function, over the stated interval, find the requested value.
104)
f(x) =1
7, over the interval 2 x 10. Find E(x).
104)
A)
992
21
B)
48
7
C)
96
7
D)
95
14
Provide an appropriate response.
105)
A physical fitness association is including the mile run in its secondary–school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 440 seconds and a standard deviation of 50 seconds. Find the probability that a randomly
selected boy in secondary school will take longer than 325 seconds to run the mile.
105)
A)
0.0107
B)
0.9893
C)
0.4893
D)
0.5107
106)
F(x) = f(x)
106)
A)
True
B)
False
Provide an appropriate response.
107)
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the
amount of beer poured by this filling machine follows a normal distribution with a mean of 12.14
onces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more
than 12.14 ounces of beer.
107)
A)
0.5
B)
0.4
C)
0
D)
1
Use the Poisson Distribution to find the indicated probability.
108)
If the random variable x has a Poisson Distribution with =4, find p3.
108)
A)
0.04884
B)
0.19537
C)
0.24421
D)
0.53106
Determine whether the function is a probability density function over the given interval.
109)
f(x) =8x, 0 x 2
109)
A)
No
B)
Yes
Provide an appropriate response.
110)
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the
amount of beer poured by this filling machine follows a normal distribution with a mean of
12.22 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains
between 12.12 and 12.18 ounces.
110)
A)
0.1649
B)
0.1525
C)
0.8351
D)
0.8475
111)
Suppose X is a normal random variable with density function f(x) =1
2e(–1/2)(x + 4)2. Find the
expected value and standard deviation of X.
111)
A)
µ = 1, = 16
B)
µ = – 4, = 16
C)
µ = – 4, = 1
D)
µ = 1, = 4
E)
µ = 4, = 1
Determine whether the function is a probability density function over the given interval.
112)
f(x) =3
64 x2,0 x 4
112)
A)
No
B)
Yes
Solve the problem.
113)
A dart is thrown at a number line in such a way that it always lands in the interval [0, 7]. Let x be
the number the dart hits. Suppose the probability density function for x is given by
f(x) =3
343x2, for 0 x 7.
Find P(4 x 6), the probability that it lands in [4, 6].
113)
A)
0.29
B)
0.06
C)
0.01
D)
0.44
Provide an appropriate response.
114)
A physical fitness association is including the mile run in its secondary–school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 440 seconds and a standard deviation of 40 seconds. Find the probability that a randomly
selected boy in secondary school can run the mile in less than 348 seconds.
114)
A)
0.9893
B)
0.5107
C)
0.0107
D)
0.4893
Find k such that the function is a probability density function over the given interval. Then write the probability density
function.
115)
f(x) = k(4– x); 0 x 4
115)
A)
1
8; f(x) =1
8(4 – x)
B)
16; f(x) =16(4 – x)
C)
4; f(x) =4(4 – x)
D)
1
16 ; f(x) =1
16 (4 – x)
Let X be a continuous random variable A
X
B and let f (x) be its probability density function and F (x) its cumulative
distribution function. Indicate whether the following statements are true or false.
116)
Pr(a X b) =
b
a
f(x)dx
116)
A)
True
B)
False
Determine whether the function is a probability density function over the given interval.
117)
f(x) =1
32 x, 0 x 8
117)
A)
Yes
B)
No
For the given probability density function, over the stated interval, find the requested value.
118)
f(x) =1
5x2, over the interval –2 x 3. Find E(x).
118)
A)
73
20
B)
13
4
C)
81
20
D)
71
20
Find k such that the function is a probability density function over the given interval. Then write the probability density
function.
119)
f(x) =k
x; 1 x 11
119)
A)
ln 11; f(x) = x ln 11
B)
1
ln 11 ; f(x) =1
x ln 11
C)
2
ln 11 ; f(x) =2
x ln 11
D)
1 – ln 11; f(x) =x
1 – ln 11
120)
A random variable X has a cumulative distribution function F(x) = 1 –1
x2 (x 1). Find Pr(a X 5).
120)
A)
24
25 –1
a2
B)
1
a2
C)
1
a2–1
25
D)
1 –1
a2
E)
none of these
Solve the problem.
121)
The number of new mini–vans sold by a particular salesperson during the month of March is
exponentially distributed with a mean of 10. What is the probability that the salesperson will sell
between 4 and 7 mini–vans in March?
121)
A)
0.114
B)
0.173
C)
0.174
D)
0.203
27
Let X be a continuous random variable on a
x b with probability density function f(x). Then the median of the x–values
is that number m for which
m
a
f(x) dx =1
2.
Find the median.
122)
f(x) =x
8–1
2; 4 x 8
122)
A)
6.83
B)
0.50
C)
6
D)
5.41
Determine the area under the standard normal curve that lies between:
123)
z = – 0.3 and z =0.3
123)
A)
0.3821
B)
0.6179
C)
0.5
D)
0.2358
Solve the problem.
124)
A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x be
the number the dart hits. Suppose the probability density function for x is given by
f(x) =x
50 , for 0 x 10.
Find P(2 x 5), the probability that it lands in [2, 5].
124)
A)
0.03
B)
0.21
C)
0.09
D)
0.42
125)
The table below is the probability table for a random variable X. Find E(X), Var(X), and the
standard deviation of X.
Outcome –2–1 0 1 2
Probability 0.2 0.35 0.15 0.05 0.25
125)
A)
E(X) = – 0.2; Var(X) = 0; standard deviation of X = 0
B)
E(X) = – 0.2; Var(X) = 2.22; standard deviation of X =1.49
C)
E(X) = – 0.2; Var(X) = 4; standard deviation of X =2
D)
E(X) = – 0.2; Var(X) = 2.16; standard deviation of X =1.47
E)
none of these
Find k such that the function is a probability density function over the given interval. Then write the probability density
function.
126)
f(x) = k; 2 x 7
126)
A)
2; f(x) =2
B)
1
2; f(x) =1
2
C)
5; f(x) =5
D)
1
5; f(x) =1
5
127)
A random variable X is exponentially distributed with a mean of 2. Find Pr(1 X 3).
127)
A)
1
2e–1/2
B)
1
2e–3/2
C)
1
2(e–1–e–3)
D)
e–1/2 –e–3/2
E)
none of these
29
Answer Key
Testname: C12
Answer Key
Testname: C12
31
Answer Key
Testname: C12
32
Answer Key
Testname: C12