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 stock price beyond which 0.05 of the distribution falls is _________.
A) $ 4.60
B) $12.47
C) $ 4.57
D) $12.44

Question

Quizplus · Accepted Answer

Using the normal distribution table or calculator, we can find the z-score that corresponds to 0.05 in the tail of the distribution to be approximately 1.645. We can then use the formula z = (x - μ) / σ and solve for x to find the stock price beyond which 0.05 of the distribution falls:
1.645 = (x - 8.52) / 2.38
x - 8.52 = 3.9181
x = 12.4381 or approximately $12.44.
Therefore, the answer is D.

A Stockbroker Has Kept a Daily Record of the Value