Suppose you observe a data point x 12 and it is known that

Suppose you observe a data point x = 12 and it is known that this data point came from a normal distribution with mean 5 and standard deviation 2. Which of the following statements is true regarding the observation of x = 12? (0.5 point)

a) The observation would not be considered unusual, because we know exactly which normal distribution it comes from.

b) The observation would be considered unusual because it is farther than three standard deviations from the mean.

c) The observation would be considered unusual because x = 12 is over twice as large as the mean of the distribution.

d) The observation would not be considered unusual because it is only about three standard deviations from the mean.

Solution

ANSWER: OPTION B

b) The observation would be considered unusual because it is farther than three standard deviations from the mean.

Note that from your empirical rule, only 0.3% is farther than 3 standard deviations from the mean. THat\'s indeed unusual!