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. What percentage of the distribution lies below $7.42.
A) 17.72%
B) 32.28%
C) 82.28%
D) 31.92%

Question

Quizplus · Accepted Answer

We need to use the z-score formula to solve this problem:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, σ is the standard deviation, and z is the corresponding z-score.

In this case, x = $7.42, μ = $8.52, and σ = $2.38. Plugging these values into the formula, we get:

z = (7.42 - 8.52) / 2.38 = -0.46

To find the percentage of the distribution that lies below $7.42, we need to find the area to the left of the z-score of -0.46 on the standard normal distribution table (also known as the z-table).

Looking up -0.46 on the z-table, we find the area to the left of it is 0.3228 or 32.28% (rounded to two decimal places).

Therefore, the answer is B.

A Stockbroker Has Kept a Daily Record of the Value