Question

he average return for large-cap domestic stock funds over three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%. (a) What is the probability an individual large-cap domestic stock fund had a three-year return of at least 19%

Answer 1

Answer:

14.81% probability an individual large-cap domestic stock fund had a three-year return of at least 19%

Step-by-step explanation:

Problems of normally distributed samples are 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:

$\mu = 0.144, \sigma = 0.044$

What is the probability an individual large-cap domestic stock fund had a three-year return of at least 19%

This is 1 subtracted by the pvalue of Z when X = 0.19. So

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

$Z = \frac{0.19 - 0.144}{0.044}$

$Z = 1.045$

$Z = 1.045$ has a pvalue of 0.8519

1 - 0.8519 = 0.1481

14.81% probability an individual large-cap domestic stock fund had a three-year return of at least 19%