The time required for a citizen to complete the 2010 U.S.Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes.The slowest 10 percent of the citizens would need at least how many minutes to complete the form?
A)27.2
B)35.8
C)52.8
D)59.6

Question

Quizplus · Accepted Answer

We need to find the time taken by the slowest 10 percent of citizens, which means we need to find the 10th percentile. Using a standard normal distribution table or a calculator, we find the z-score corresponding to the 10th percentile is approximately -1.28. We can use the formula z = (x - mu) / sigma to find the corresponding time x, where mu is the mean time, sigma is the standard deviation, and x is the time needed. Plugging in the given values, we get -1.28 = (x - 40) / 10. Solving for x, we get x = 52.8 minutes. Therefore, the slowest 10 percent of citizens would need at least 52.8 minutes to complete the form, which is choice C.

The Time Required for a Citizen to Complete the 2010