A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.50, 0.38, 0.10, and 0.02, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth.

A) $\sigma = 0.55$
B) $\sigma = 1.02$
C) $\sigma = 0.74$
D) $\sigma = 0.98$

Question

A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.50, 0.38, 0.10, and 0.02, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth.

A) $\sigma = 0.55$
B) $\sigma = 1.02$
C) $\sigma = 0.74$
D) $\sigma = 0.98$

Quizplus · Accepted Answer

First, calculate the mean: $ \mu = 0(0.50) + 1(0.38) + 2(0.10) + 3(0.02) = 0.64 $. Then, calculate the variance: $ \sigma^2 = (0-0.64)^2(0.50) + (1-0.64)^2(0.38) + (2-0.64)^2(0.10) + (3-0.64)^2(0.02) = 0.5472 $. Finally, the standard deviation is $ \sigma = \sqrt{0.5472} \approx 0.74 $.

A Police Department Reports That the Probabilities That 0, 1 σ=0.55\sigma = 0.55σ=0.55

A Police Department Reports That the Probabilities That 0, 1 $\sigma = 0.55$