Question

Suppose that the distribution of scores on an exam can be described by a normal curve with mean 110. The 16th percentile of this distribution is 90. (Use the Empirical Rule.)

(a) What is the 84th percentile?
(b) What is the approximate value of the standard deviation of exam scores

Answer 1

The 84th percentile is 130, and the approximate value for the standard deviation of the exam scores is 20, based on the Empirical Rule and the given data of the 16th percentile.

Step-by-step explanation:

The question given is about finding the 84th percentile and the standard deviation of exam scores based on the information that the 16th percentile is 90 with a mean of 110. Since the distribution is normal, we can use the Empirical Rule.

(a) To find the 84th percentile, we note that it is symmetrically opposite the 16th percentile in a normal distribution. Because the distance between the mean and the 16th percentile corresponds to the space below one standard deviation from the mean, the same distance above the mean will give us the 84th percentile. Hence, the 84th percentile is 110 + (110 - 90) = 130.

(b) To estimate the standard deviation, we use the fact that the 16th percentile (90) is one standard deviation below the mean (110). Thus, one standard deviation is approximately 110 - 90 = 20.