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The mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 41 millimeters. Assume these lengths are normally distributed. What proportion of six-year-old rainbow trout are less than 516 millimeters long?

Respuesta :

JeanaShupp

Answer: 0.8023

Step-by-step explanation:

Given : [tex]\text{Mean}=\mu=481 \text{ millimeters}[/tex]

[tex]\text{Standard deviation}=41 \text{ millimeters}[/tex]

Assuming these lengths are normally distributed.

The formula to calculate the z-score is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= [tex]516 \text{ millimeters}[/tex]

[tex]z=\dfrac{516-481}{41}=0.853658536585\approx0.85[/tex]

The p-value = [tex]P(z\leq0.85)=0.8023374\approx0.8023[/tex]

Hence, the required probability : 0.8023

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