A group of mutual funds earned varying annual rates of return in the last year. These rates of return are normally distributed with a mean of 9% and a standard deviation of 16%.One mutual fund in this group managed to earn a rate of return that was double that of this group's average that year. This performance would put the fund in the top X% of those funds in that year.Calculate X%. Give your answer to 1 decimal place.

The mutual friend in in the top 28.8%. So X% = 28.8%.

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:

One mutual fund in this group managed to earn a rate of return that was double that of this group's average that year. This performance would put the fund in the top X% of those funds in that year.Calculate X%.

Here we have

Top X%

X is 1 subtracted by the pvalue of Z when X = 0.18. So

has a pvalue of 0.712.

100 - 71.2 = 28.8%

The mutual friend in in the top 28.8%. So X% = 28.8%.