the lengths of the red drum species of fish are approximately normally distributed, with a mean length of 24…

the lengths of the red drum species of fish are approximately normally distributed, with a mean length of 24 inches and a standard deviation of 1.4 inches. what proportion of red drum fish are less than 23 inches in length? find the z - table here. 0.1587 0.2389 0.2709 0.7611

the lengths of the red drum species of fish are approximately normally distributed, with a mean length of 24 inches and a standard deviation of 1.4 inches. what proportion of red drum fish are less than 23 inches in length? find the z - table here. 0.1587 0.2389 0.2709 0.7611

Answer

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 23$ (the value of interest), $\mu = 24$ (the mean), and $\sigma=1.4$ (the standard deviation). $z=\frac{23 - 24}{1.4}=\frac{- 1}{1.4}\approx - 0.71$

Step2: Find the proportion from the z - table

Looking up the z - score of $-0.71$ in the standard normal (z) table, we find the proportion of values to the left of this z - score. The value from the z - table for $z=-0.71$ is $0.2389$.

Answer:

0.2389