For a normal distribution, with a mean of 10, if approximately 16% of the observations lie above a score of 13, what is the VARIANCE of the distribution?
A) .3
B) 9
C) 13
D) 19

Question

Quizplus · Accepted Answer

Since we know that the mean is 10, we can use the standard normal distribution table to find the corresponding z-score for an observation of 13.

Using the table, we find that the z-score for an observation of 13 is approximately 0.84.

Since we know that 16% of the observations lie above 13, we know that the area under the curve to the right of 0.84 is 0.16.

Using the standard normal distribution table again, we can find the z-score that corresponds to an area of 0.16 to the right of it, which is approximately 1.00.

Therefore, the standard deviation of the distribution is (13-10)/1.00 = 3, and the variance is 3^2 = 9.

So the best choice is B.

For a Normal Distribution, with a Mean of 10, If