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 between $5 and $11?
A) 21.48%
B) 78.41%
C) 49.41%
D) 57.98%

Question

Quizplus · Accepted Answer

To find the percentage of the distribution that lies between $5 and $11, we need to standardize the values using the formula:
z = (x - mean) / standard deviation

For x = $5:
z = (5 - 8.52) / 2.38 = -1.48

For x = $11:
z = (11 - 8.52) / 2.38 = 1.04

Using a standard normal table or calculator, we can find the probability that z lies between -1.48 and 1.04, which is approximately 0.7841 or 78.41%.

A Stockbroker Has Kept a Daily Record of the Value