In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below. x P(x) 0 0.261 1 0.569 2 0.135 3 0.031 4 0.003 5 0.001 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because all of the probabilities are all of the probabilities are at least one of the probabilities is between nothing and nothing, inclusive, and the mean of the probabilities is nothing. (Type whole numbers. Use ascending order.) (b) Draw a graph of the probability distribution. Describe the shape of the distribution. Graph the probability distribution. Choose the correct graph below. A. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.03; 1, 0; 2, 0; 3, 0.26; 4, 0.57; 5, 0.14. B. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.26; 1, 0.57; 2, 0.14; 3, 0.03; 4, 0; 5, 0. C. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.57; 1, 0.03; 2, 0; 3, 0.26; 4, 0.14; 5, 0. D. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0; 1, 0; 2, 0.03; 3, 0.14; 4, 0.57; 5, 0.26. Describe the shape of the distribution. The distribution ▼ is uniform is multimodal has one mode is bimodal and is ▼ skewed left. skewed right. roughly symmetric. (c) Compute and interpret the mean of the random variable X. μX=nothing marriages (Type an integer or a decimal. Do not round.) Which of the following interpretations of the mean is correct?
In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below. x P(x) 0 0.261 1 0.569 2 0.135 3 0.031 4 0.003 5 0.001 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because all of the probabilities are all of the probabilities are at least one of the probabilities is between nothing and nothing, inclusive, and the mean of the probabilities is nothing. (Type whole numbers. Use ascending order.) (b) Draw a graph of the probability distribution. Describe the shape of the distribution. Graph the probability distribution. Choose the correct graph below. A. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.03; 1, 0; 2, 0; 3, 0.26; 4, 0.57; 5, 0.14. B. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.26; 1, 0.57; 2, 0.14; 3, 0.03; 4, 0; 5, 0. C. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.57; 1, 0.03; 2, 0; 3, 0.26; 4, 0.14; 5, 0. D. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0; 1, 0; 2, 0.03; 3, 0.14; 4, 0.57; 5, 0.26. Describe the shape of the distribution. The distribution ▼ is uniform is multimodal has one mode is bimodal and is ▼ skewed left. skewed right. roughly symmetric. (c) Compute and interpret the mean of the random variable X. μX=nothing marriages (Type an integer or a decimal. Do not round.) Which of the following interpretations of the mean is correct?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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(a) Verify that this is a discrete probability distribution.
This is a discrete probability distribution because
between
of the probabilities is
all of the probabilities are
all of the probabilities are
at least one of the probabilities is
nothing
and
nothing,
inclusive, and the
mean
nothing.
(Type whole numbers. Use ascending order.)
(b) Draw a graph of the probability distribution. Describe the shape of the distribution.
Graph the probability distribution. Choose the correct graph below.
Describe the shape of the distribution.
The distribution
and is
▼
is uniform
is multimodal
has one mode
is bimodal
▼
skewed left.
skewed right.
roughly symmetric.
(c) Compute and interpret the mean of the random variable X.
μX=nothing
marriages(Type an integer or a decimal. Do not round.)
Which of the following interpretations of the mean is correct?
The observed number of marriages will be equal to the mean number of marriages for most individuals.
The observed number of marriages will be less than the mean number of marriages for most individuals.
If any number of individuals aged 15 year or older were surveyed, one would expect the mean number of marriages to be the mean of the random variable.
If many individuals aged 15 year or older were surveyed, one would expect the mean number of marriages to be the mean of the random variable.
(d) Compute the standard deviation of the random variable X.
σX=nothing
marriages(Round to one decimal place as needed.)
(e) What is the probability that a randomly selected individual 15 years or older was involved in two marriages?
nothing
(Type an integer or a decimal. Do not round.)
(f) What is the probability that a randomly selected individual 15 years or older was involved in at least two marriages?
nothing
(Type an integer or a decimal. Do not round.)
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