A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. The percentile rank of a price of $13.87 is _________.
A) 48.78%
B) 1.22%
C) 98.78%
D) 51.22%

Question

Quizplus · Accepted Answer

We need to find the percentile rank of a price of $13.87, which is the percentage of prices that are less than or equal to $13.87. To do this, we can standardize the value using the formula z = (x - mu) / sigma, where x is the value we're interested in, mu is the mean, and sigma is the standard deviation. Plugging in the values, we get z = (13.87 - 8.52) / 2.38 = 2.24. We can use a standard normal distribution table or calculator to find the area to the left of this z-score, which represents the percentile rank. The area is approximately 0.9878, or 98.78%. Therefore, the answer is C.

A Stockbroker Has Kept a Daily Record of the Value