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Math Problems
Algebra 2
Find probabilities using the normal distribution I
X
X
X
is a normally distributed random variable with mean
43
43
43
and standard deviation
11
11
11
. What is the probability that
X
X
X
is between
41
41
41
and
45
45
45
? Write your answer as a decimal rounded to the nearest thousandth.
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X
X
X
is a normally distributed random variable with mean
29
29
29
and standard deviation
11
11
11
. What is the probability that
X
X
X
is between
4
4
4
and
54
54
54
? Write your answer as a decimal rounded to the nearest thousandth.
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X
X
X
is a normally distributed random variable with mean
35
35
35
and standard deviation
5
5
5
. What is the probability that
X
X
X
is between
25
25
25
and
45
45
45
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
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X
X
X
is a normally distributed random variable with mean
45
45
45
and standard deviation
10
10
10
. What is the probability that
X
X
X
is between
35
35
35
and
55
55
55
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
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X
X
X
is a normally distributed random variable with mean
8
8
8
and standard deviation
5
5
5
. What is the probability that
X
X
X
is between
3
3
3
and
13
13
13
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
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X
X
X
is a normally distributed random variable with mean
38
38
38
and standard deviation
4
4
4
. What is the probability that
X
X
X
is between
26
26
26
and
50
50
50
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
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X
X
X
is a normally distributed random variable with mean
34
34
34
and standard deviation
6
6
6
. What is the probability that
X
X
X
is between
16
16
16
and
52
52
52
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
Get tutor help
X
X
X
is a normally distributed random variable with mean
44
44
44
and standard deviation
13
13
13
. What is the probability that
X
X
X
is between
5
5
5
and
83
83
83
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
Get tutor help
X
X
X
is a normally distributed random variable with mean
43
43
43
and standard deviation
18
18
18
. What is the probability that
X
X
X
is between
25
25
25
and
61
61
61
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
Get tutor help
X
X
X
is a normally distributed random variable with mean
94
94
94
and standard deviation
5
5
5
. What is the probability that
X
X
X
is between
89
89
89
and
99
99
99
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
Get tutor help
X
X
X
is a normally distributed random variable with mean
93
93
93
and standard deviation
1
1
1
. What is the probability that
X
X
X
is between
90
90
90
and
96
96
96
? Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
Get tutor help
X
X
X
is a normally distributed random variable with mean
10
10
10
and standard deviation
3
3
3
. What is the probability that
X
X
X
is between
9
9
9
and
11
11
11
? Write your answer as a decimal rounded to the nearest thousandth.
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X
X
X
is a normally distributed random variable with mean
18
18
18
and standard deviation
2
2
2
. What is the probability that
X
X
X
is between
17
17
17
and
19
19
19
? Write your answer as a decimal rounded to the nearest thousandth.
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A continuous random variable,
X
X
X
, has probability density function given by:
\newline
f
(
x
)
=
{
k
(
x
−
3
)
3
⩽
x
<
7
k
(
11
−
x
)
7
⩽
x
⩽
11
0
otherwise
\mathrm{f}(x)=\left\{\begin{array}{ll}k(x-3) & 3 \leqslant x<7 \\ k(11-x) & 7 \leqslant x \leqslant 11 \\ 0 & \text { otherwise }\end{array}\right.
f
(
x
)
=
⎩
⎨
⎧
k
(
x
−
3
)
k
(
11
−
x
)
0
3
⩽
x
<
7
7
⩽
x
⩽
11
otherwise
\newline
a Show that
k
=
16
.
16
k=\frac{16}{.16}
k
=
.16
16
.
\newline
[
3
3
3
]
\newline
c Find the value of
a
a
a
if
P
(
3
⩽
X
⩽
a
)
=
0.75
\mathrm{P}(3 \leqslant X \leqslant a)=0.75
P
(
3
⩽
X
⩽
a
)
=
0.75
.
\newline
[
3
3
3
]
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A bag contains
4
4
4
blue and
8
8
8
green marbles. Three marbles are selected at random from the bag.
\newline
a. If the first marble is replaced before the second marble is drawn what is
P
\mathrm{P}
P
(blue second I green first)? Use the conditional probability formula!
\newline
b. If the first marble is NOT replaced what is P(blue second / green first)? Use conditional probability formula!
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A study was commissioned to find the mean weight of the residents in certain town. The study examined a random sample of
61
61
61
residents and found the mean weight to be
166
166
166
pounds with a standard deviation of
37
37
37
pounds. At the
95
%
95 \%
95%
confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest tenth. (Do not write
±
\pm
±
).
\newline
Answer:
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X
X
X
is a normally distributed random variable with mean
65
65
65
and standard deviation
8
8
8
.
\newline
What is the probability that
X
X
X
is between
62
62
62
and
68
68
68
?
?
?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
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X
X
X
is a normally distributed random variable with mean
49
49
49
and standard deviation
25
25
25
.
\newline
What is the probability that
X
X
X
is between
24
24
24
and
74
74
74
?
?
?
\newline
Use the
0.68
−
0.95
−
0.997
0.68-0.95-0.997
0.68
−
0.95
−
0.997
rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
\newline
____
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