The lengths of trout in a lake are normally distributed with a mean of 30 inches and a standard deviation of 4.5 inches. enter the z-score of a trout with a length of 28.2 inches.

We have been given that the lengths of trout in a lake are normally distributed with a mean of 30 inches and a standard deviation of 4.5 inches.

We are asked to find the z-score of a trout with a length of 28.2 inches.

To find z score of the given length  we will use z score formula.

, where x is the given value of which we want to find out z score, is mean of the given data and is standard deviation of data.

After substituting our given values in this formula we will get,

Therefore, z  score of a trout with a length of 28.2 inches is -0.4.

a - base

b - exponent

so,