Question
Following is the probability distribution for age of a student at a certain public high school....
Following is the probability distribution for age of a student at a certain public high school.
|
x |
13 |
14 |
15 |
16 |
17 |
18 |
|---|---|---|---|---|---|---|
|
Px |
0.09 |
0.23 |
0.25 |
0.26 |
0.14 |
0.03 |
(a) Find the variance of the ages. Round the answer to at least
four decimal places.
The variance of the ages is?
(b) Find the standard deviation of the ages.
Homework Answers
Answer #1
Solution:
| x | P(x) | x * P(x) | x2 * P(x) |
| 13 | 0.09 | 1.17 | 15.21 |
| 14 | 0.23 | 3.22 | 45.08 |
| 15 | 0.25 | 3.75 | 56.25 |
| 16 | 0.26 | 4.16 | 66.56 |
| 17 | 0.14 | 2.38 | 40.46 |
| 18 | 0.03 | 0.54 | 9.72 |
| Sum | 1 | 15.22 | 233.28 |
Mean = 
X * P(X)
= 15.22
Variance
=
X 2 * P(X) -
2
= 233.28 - (15.22)2 = 1.6316
The variance of the ages is 1.6316
Standard deviation = 
= 1.2773
The standard deviation of the ages is 1.2773
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