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Math Problems
Precalculus
Find values of normal variables
A spinner is divided into
5
5
5
equal sections. When the spinner is spun, what is the probability of the events listed below?
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2
2
2
The random variable
X
X
X
has mean
372
372
372
and standard deviation
54
54
54
.
\newline
(i) Describe fully the distribution of the mean of a random sample of
36
36
36
values of
X
X
X
.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
66
66
66
and standard deviation
20
20
20
, the bottom
40
%
40\%
40%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
38
38
38
and standard deviation
9
9
9
, the bottom
10
%
10\%
10%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
54
54
54
and standard deviation
17
17
17
, the bottom
20
%
20\%
20%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
41
41
41
and standard deviation
4
4
4
, the bottom
20
%
20\%
20%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
37
37
37
and standard deviation
25
25
25
, the bottom
60
%
60\%
60%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
87
87
87
and standard deviation
11
11
11
, the bottom
70
%
70\%
70%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
48
48
48
and standard deviation
19
19
19
, the bottom
30
%
30\%
30%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
63
63
63
and standard deviation
7
7
7
, the bottom
30
%
30\%
30%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
52
52
52
and standard deviation
25
25
25
, the bottom
90
%
90\%
90%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
22
22
22
and standard deviation
10
10
10
, the bottom
70
%
70\%
70%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
64
64
64
and standard deviation
13
13
13
, the bottom
40
%
40\%
40%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
72
72
72
and standard deviation
8
8
8
, the bottom
10
%
10\%
10%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
53
53
53
and standard deviation
10
10
10
, the bottom
20
%
20\%
20%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
10
10
10
and standard deviation
7
7
7
, the bottom
30
%
30\%
30%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
50
50
50
and standard deviation
20
20
20
, the bottom
20
%
20\%
20%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
43
43
43
and standard deviation
5
5
5
, the bottom
80
%
80\%
80%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
28
28
28
and standard deviation
20
20
20
, the bottom
10
%
10\%
10%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
36
36
36
and standard deviation
16
16
16
, the bottom
20
%
20\%
20%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
98
98
98
and standard deviation
13
13
13
, the bottom
90
%
90\%
90%
of the values are those less than ___.
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Complete the statement. Round your answer to the nearest thousandth.
\newline
In a population that is normally distributed with mean
64
64
64
and standard deviation
7
7
7
, the bottom
90
%
90\%
90%
of the values are those less than ___.
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1
1
1
) (
1
1
1
point) Use your knowledge of dice to generate a theoretical probability distribution of the possible sums obtained when rolling two dice. The first two rows have been completed for you.
\newline
Sum of dice
(
X
)
(\mathrm{X})
(
X
)
\# of ways of obtaining sum Relative Frequency of
(
X
)
=
(\mathrm{X})=
(
X
)
=
\newline
\quad
1
1
1
way
(
1
+
1
)
1
/
36
(1+1) \quad 1 / 36
(
1
+
1
)
1/36
\newline
\quad
2
2
2
ways
(
1
+
2
,
2
+
1
)
2
/
36
(1+2,2+1) \quad 2 / 36
(
1
+
2
,
2
+
1
)
2/36
\newline
2
2
2
) (
1
1
1
points) Use the theoretical data to calculate the mean, variance, and standard deviation of the theoretical probability distribution.
\newline
3
3
3
) (
1
1
1
point) Find the theoretical probability of rolling a sum less than
3
3
3
.
\newline
4
4
4
) (
1
1
1
point) Find the theoretical probability of rolling a sum between (and including)
4
4
4
and
7
7
7
.
\newline
5
5
5
) (
1
1
1
point) Visit the following website: http://www.dicesimulator.com/
\newline
and simulate
50
50
50
rolls of two dice (or physically roll two dice
50
50
50
times) and record your sums in the table below. You may also physically roll two dice
50
50
50
times and record your sums.
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In a recent study of
35
35
35
freshman, the mean number of hours per week that they played video games was
16
16
16
.
6
6
6
. Assume the population standard deviation is
2
2
2
.
8
8
8
. Determine the
99
%
99 \%
99%
confidence interval. Round your values to the nearest thousandth.
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You are dealt one card from a
52
52
52
-card deck. Find the probability that you are not dealt an ace.
\newline
The probability is
□
\square
□
(Type an integer or a fraction. Simplify your answer.)
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The weather forecaster says that tomorrow there is a
94
%
94 \%
94%
chance that it will rain. Which word or phrase describes the probability that it will rain?
\newline
unlikely
\newline
likely
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
certain
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Question
\newline
Suppose heights of dogs, in inches, in a city are normally distributed and have a known population standard deviation of
7
7
7
inches and an unknown population mean. A random sample of
15
15
15
dogs is taken and gives a sample mean of
34
34
34
inches. Find the confidence interval for the population mean with a
99
%
99 \%
99%
confidence level.
\newline
\begin{tabular}{|c|c|c|c|c|}
\newline
\hline
z
0.10
\mathbf{z}_{0.10}
z
0.10
&
z
0.05
\mathbf{z}_{0.05}
z
0.05
&
z
0.025
\mathbf{z}_{0.025}
z
0.025
&
z
0.01
\mathbf{z}_{0.01}
z
0.01
&
z
0.005
\mathbf{z}_{0.005}
z
0.005
\\
\newline
\hline
1
1
1
.
282
282
282
&
1
1
1
.
645
645
645
&
1
1
1
.
960
960
960
&
2
2
2
.
326
326
326
&
2
2
2
.
576
576
576
\\
\newline
\hline
\newline
\end{tabular}
\newline
You may use a calculator or the common
z
z
z
values above.
\newline
- Round all calculations to three decimal places, if necessary.
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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
33
33
33
residents and found the mean weight to be
162
162
162
pounds with a standard deviation of
35
35
35
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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A study was commissioned to find the mean weight of the residents in certain town. The study examined a random sample of
103
103
103
residents and found the mean weight to be
159
159
159
pounds with a standard deviation of
33
33
33
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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A study was commissioned to find the mean weight of the residents in certain town. The study examined a random sample of
33
33
33
residents and found the mean weight to be
166
166
166
pounds with a standard deviation of
26
26
26
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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A study was commissioned to find the mean weight of the residents in certain town. The study examined a random sample of
45
45
45
residents and found the mean weight to be
191
191
191
pounds with a standard deviation of
28
28
28
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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There is a
3
%
3 \%
3%
probability that a selected life insurance application contains an error. An auditor randomly selects
100
100
100
applications. Using the Poisson approximation to the Binomial, calculate the probability that
9
5
1
/
%
95_{1} / \%
9
5
1
/%
or less of the applications are error-free.
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Nate predicted that voter turnout for the next citywide election will be
23
%
23\%
23%
, with a margin of error of
3
%
3\%
3%
. Which of the following represents the plausible range of voter turnout based on Nate's prediction and margin of error?
\newline
Choose
1
1
1
answer:
\newline
(A) Between
20
%
20\%
20%
and
26
%
26\%
26%
\newline
(B) Between
21.5
%
21.5\%
21.5%
and
24.5
%
24.5\%
24.5%
\newline
(C) Between
23
%
23\%
23%
and
26
%
26\%
26%
\newline
(D) Between
23
%
23\%
23%
and
29
%
29\%
29%
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