Answer to Question #311888 in Statistics and Probability for apple

Question

The probabilities that a traffic inspector will discover violations of the Traffic Code in Davao City are given in the following table.

Number of Violations (X)

Probability P(X)

0.41

1

2

3

0.22

0.17

4

5

0.13

0.05

0.02

a. Solve for the mean and variance. b. Interpret the mean and the variance of the problem.

Answer 1

Solution

Mean

$\mu_x=\sum XP(X)$

$\mu_x=[0(0.41)+1(0.22)+2(0.17)+3(0.13)+4(0.05)+5(0.02)]$

$\mu_x=1.25$

Variance

$\sigma^2=\sum X^2.P(X)-\mu^2$

$\sigma^2=[0(0.41)+1^2(0.22)+2^2(0.17)+3^2(0.13)+4^2(0.05)+5^2(0.02)]-1.25^2$

$\sigma^2=3.37-1.5625$

$\sigma^2=1.8075$

The mean is small (1.25) and closer to the lower numbers (0 1 and 2) due to their larger probability compared to the other numbers (3 4 and 5)

The variance is relatively small (1.8075) indicating that the results are close to each other.