The average size of a rainbow trout in Red Fish Lake is normally distributed with mean 11.7 inches and a standard deviation of 3.9 inches. (a). What is the probability that the next fish caught is at least 16 inches long

13.57% probability that the next fish caught is at least 16 inches long

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 that the next fish caught is at least 16 inches long

This is 1 subtracted by the pvalue of Z when X = 16. So

has a pvalue of 0.8643

1 - 0.8643 = 0.1357

13.57% probability that the next fish caught is at least 16 inches long