Solution Found!
Finding the Mean, Variance, and Standard Deviation In
Chapter 4, Problem 29E(choose chapter or problem)
(a) Find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results.
The number of dogs per household in a small town
\(\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Dogs } & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Probability } & 0.686 & 0.195 & 0.077 & 0.022 & 0.013 & 0.007 \\ \hline \end{array}\)
Questions & Answers
QUESTION:
(a) Find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results.
The number of dogs per household in a small town
\(\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Dogs } & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Probability } & 0.686 & 0.195 & 0.077 & 0.022 & 0.013 & 0.007 \\ \hline \end{array}\)
ANSWER:Step 1 of 3
The given number of dogs per household in a small town is
|
Dogs |
0 |
1 |
2 |
3 |
4 |
5 |
|
Probability |
0.686 |
0.195 |
0.077 |
0.022 |
0.013 |
0.007 |
a). Here we have to find the mean, variance and standard deviation.
The mean is given by
\(\begin{aligned} \mu & =\sum x p(x) \\ & =0 \times 0.686+1 \times 0.195+2 \times 0.077+3 \times 0.022+4 \times 0.013+5 \times 0.007 \\ & =0+0.195+0.154+0.066+0.052+0.035 \\ & =0.502 \end{aligned}\)
Hence, mean \(\mu=0.502\).