Question

The stock price of a particular asset has a mean and standard deviation of $58.50 and $8.25, respectively. Compute the 95th percentile of this stock price.
a. $22.76
b. 1.645
c. $44.93
d. $72.07

Answer 1

Answer:

d. $72.07

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 58.5, \sigma = 8.25$

Compute the 95th percentile of this stock price.

This is X when Z has a pvalue of 0.95. So it is X when Z = 1.645.

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 58.5}{8.25}$

$X - 58.5 = 1.645*8.25$

$X = 72.07$

So the correct answer is:

d. $72.07