A college placement office conducted a survey of 100 engineers who had graduated from Stanford University.For these engineers,the mean salary was computed to be $72,000 with a standard deviation of $8,000.The percentage of these engineers who earn more than $96,000 or less than $48,000 is:
A)approximately 0%.
B)at least 5.6% (1/18 of the engineers).
C)at most 5.6% (1/18 of the engineers).
D)at most 11.1% (1/9 of the engineers).

Question

Quizplus · Accepted Answer

We need to find the percentage of engineers who earn more than $96,000 or less than $48,000.

Using the empirical rule, we can say that approximately 68% of the engineers earn salaries between $64,000 ($72,000 - one standard deviation of $8,000) and $80,000 ($72,000 + one standard deviation of $8,000).

Using the same empirical rule, we can say that approximately 95% of the engineers earn salaries between $56,000 ($72,000 - two standard deviations of $8,000) and $88,000 ($72,000 + two standard deviations of $8,000).

Since $48,000 is more than two standard deviations below the mean salary, we can say that less than 2.5% of the engineers earn salaries less than $48,000.

Similarly, since $96,000 is more than two standard deviations above the mean salary, we can say that less than 2.5% of the engineers earn salaries more than $96,000.

Therefore, the percentage of engineers who earn more than $96,000 or less than $48,000 is at most 2.5% + 2.5% = 5%, which is equivalent to 5/100 or 1/20 or 1/9. The closest answer choice to this value is D, which states that the percentage is at most 11.1% (1/9 of the engineers).

A College Placement Office Conducted a Survey of 100 Engineers