A sample of 500 evening students revealed that their annual incomes were normally distributed with a mean income of $50,000 and a standard deviation of $4,000. What is the income that separates the top 5% from the lower 95% of the incomes?
A) $43,420
B) $47,320
C) $56,580
D) $52,680

Question

Quizplus · Accepted Answer

We need to find the income that separates the top 5% from the lower 95% of the incomes. Since the distribution is normal, we can use the z-score formula. The z-score that corresponds to the top 5% of the distribution is 1.645 (found in z-score table or calculator). So, we can solve for x (the income) using the formula:
1.645 = (x - 50,000) / 4,000
x = 56,580 (rounded to the nearest dollar)
Therefore, the answer is C.

A Sample of 500 Evening Students Revealed That Their Annual