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 8?
A) 0.34
B) 0.68
C) 0.84
D) 0.01

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected town will have a homicide rate greater than 8 per 100,000 population, we first calculate the Z-score for a rate of 8 using the formula Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. Here, X = 8, μ = 10, and σ = 2. Thus, Z = (8 - 10) / 2 = -1. The Z-score of -1 corresponds to a probability of 0.1587 (from Z-tables) for a value being less than 8. Since we're interested in greater than 8, we subtract this from 1 (1 - 0.1587 = 0.8413), which gives us approximately 0.84 or 84% chance.

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