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.

Math   Statistics-And-Probability   
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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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