## Related questions with answers

The length of a certain kind of Colorado brook trout is normally distributed with a mean of 12.5 inches and a standard deviation of 1.2 inches. What minimum size limit should the Department of Natural Resources set if it wishes to allow people to keep 80 percent of the trout they catch?

Solution

VerifiedLet $X$ be the length of a certain kind of brook trout defined as:

$X\sim N(12.2,1.2)$

Measured in inches. To find the minimum size limit to allow people to keep $80$ percent of the trout they catch, we need to express this as probability notation. Then find the corresponding $z-$score using the given area and the cumulative standard normal distribution table. Finally, use the $x$ formula, which is derived from the $z$ formula:

$x=\mu+z\sigma$

to find the unknown size limit $x$.

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