In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean?
A)None of them
B)About 27
C)About 100
D)About 127

Question

Quizplus · Accepted Answer

In a normal distribution, about 99.7% of the data falls within three standard deviations of the mean. This means that 0.3% of the data lies beyond three standard deviations from the mean. For 10,000 observations, 0.3% of 10,000 is 30. However, since the distribution is on both sides of the mean, it's slightly less, making the closest estimate about 27.

In a Sample of 10,000 Observations from a Normal Population