The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2.If the variable is normally distributed,what is the probability that a randomly selected town will have a homicide rate greater than 14?
A)0.34
B)0.68
C)0.50
D)0.02

Question

Quizplus · Accepted Answer

We need to find the probability of a town having a homicide rate greater than 14, which is equivalent to finding the area under the normal curve to the right of the z-score corresponding to 14.

z = (x - μ) / σ

z = (14 - 10) / 2 = 2

Using the standard normal distribution table or calculator, we can find that the probability of a z-score being greater than 2 is approximately 0.0228.

Therefore, the probability of a randomly selected town having a homicide rate greater than 14 is 0.0228 or 2.28%, which corresponds to answer choice D.

The Average Homicide Rate for the Cities and Towns in a State