Many states have fishing regulations that require anglers to throw back caught fish if they do not meet length requirements. For the red drum species, a caught fish must be thrown back if it is not between 21 and 28 inches long. The lengths of the red drum species of fish have an approximately Normal distribution, with a mean length of 24 inches and a standard deviation of 1.4 inches. What proportion of red drum fish must be thrown back?

Given: The lengths of the red drum species of fish have an approximately Normal distribution, with a mean length[tex](\mu)[/tex] of 24 inches and a standard deviation[tex](\sigma)[/tex] of 1.4 inches.

Let x= length of the red drum species of fish

The probability that length is not between 21 and 28 inches long :

[tex]1-P(21<X<28)=1-P(\dfrac{21-24}{1.4}<\dfrac{X-\mu}{\sigma}<\dfrac{28-24}{1.4})\\\\=1-P(-2.14<z<2.86)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-(P(z<2.86)-P(z<-2.14))\\\\=1-(0.9979-0.01617)\\\\=1-0.98173=0.01827[/tex]

Hence, the proportion of red drum fish must be thrown back = 0.01827

dmchilders03 dmchilders03 · Answer 2 · 2021-03-26T08:22:22+01:00

dmchilders03 dmchilders03

26-03-2021

Answer:

option b on edge

Step-by-step explanation:

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