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Solved: Televisions In the Sullivan Statistics Survey,
Chapter 11, Problem 17AYU(choose chapter or problem)
Problem 17AYU
Televisions In the Sullivan Statistics Survey, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.
Number of Televisions, x |
P(x) |
0 |
0 |
1 |
0.161 |
2 |
0.261 |
3 |
0.176 |
4 |
0.186 |
5 |
0.116 |
6 |
0.055 |
7 |
0.025 |
8 |
0.010 |
9 |
0.010 |
(a) Verify this is a discrete probability distribution.
(b) Draw a probability histogram.
(c) Determine and interpret the mean of the random variable X.
(d) Determine the standard deviation of the random variable X.
(e) What is the probability that a randomly selected household has three televisions?
(f) What is the probability that a randomly selected household has three or four televisions?
(g) What is the probability that a randomly selected household has no televisions? Would you consider this to be an impossible event?
Questions & Answers
QUESTION:
Problem 17AYU
Televisions In the Sullivan Statistics Survey, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.
Number of Televisions, x |
P(x) |
0 |
0 |
1 |
0.161 |
2 |
0.261 |
3 |
0.176 |
4 |
0.186 |
5 |
0.116 |
6 |
0.055 |
7 |
0.025 |
8 |
0.010 |
9 |
0.010 |
(a) Verify this is a discrete probability distribution.
(b) Draw a probability histogram.
(c) Determine and interpret the mean of the random variable X.
(d) Determine the standard deviation of the random variable X.
(e) What is the probability that a randomly selected household has three televisions?
(f) What is the probability that a randomly selected household has three or four televisions?
(g) What is the probability that a randomly selected household has no televisions? Would you consider this to be an impossible event?
ANSWER:
Problem 17AYU
Answer:
Step1 of 1:
We have In the Sullivan Statistics Survey, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.
Number of Televisions, x |
P(x) |
0 |
0 |
1 |
0.161 |
2 |
0.261 |
3 |
0.176 |
4 |
0.186 |
5 |
0.116 |
6 |
0.055 |
7 |
0.025 |
8 |
0.01 |
9 |
0.01 |
a).
Each probability is between 0 and 1, inclusive, and the sum of the probabilities equals 1.hence this is a discrete probability distribution.
b).
A probability histogram is obtained by using excel and steps are as follows:
Enter all given data in Excel sheet
select probabilities colum