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%

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 and standard deviation , the zscore of a measure X is given by:

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:

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

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%

1.5%

step-by-step explanation: