The annual income of residents in a certain county is Normally distributed, with a mean of $42,000 and a standard deviation of $10,000. What is the probability that a randomly chosen resident has income over $52,000?
A) 16%
B) 32%
C) 50%
D) 68%

Question

Quizplus · Accepted Answer

We need to find the probability that a randomly chosen resident has income over $52,000. We can use the z-score formula to find this probability:

z = (x - μ) / σ

where x is the value we are interested in (in this case $52,000), μ is the mean ($42,000), and σ is the standard deviation ($10,000).

z = (52,000 - 42,000) / 10,000
z = 1

Using a z-table, we can find that the probability of a standard Normal distribution with a z-score of 1 or greater is approximately 0.1587. This means that the probability of a resident in this county having income over $52,000 is approximately 0.1587 or 15.87%. Rounded to the nearest whole percent, this is 16%, which is choice A.

The Annual Income of Residents in a Certain County Is