The annual income of residents in a county is $42,000 with a standard deviation of $10,000. Between what two values do 95% of the incomes of county residents lie?
A) $40,000 and $44,000
B) $22,000 and $62,000
C) $32,000 and $52,000
D) $30,000 and $50,000

Question

Quizplus · Accepted Answer

To find the range in which 95% of the incomes lie, we can use the empirical rule (68-95-99.7 rule) which states that for a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Therefore, we calculate the range as: Mean ± 2(Standard Deviation) = $42,000 ± 2($10,000) = $42,000 ± $20,000 = $22,000 to $62,000.

The Annual Income of Residents in a County Is $42,000