Question

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?

Answer 1

Answer: 0.8023

Explanation:

Given :
`\text{Mean}=\mu=481 \text{ millimeters}`

`\text{Standard deviation}=41 \text{ millimeters}`

Assuming these lengths are normally distributed.

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

`z=(x-\mu)/(\sigma)`

For x=
`516 \text{ millimeters}`

`z=(516-481)/(41)=0.853658536585\approx0.85`

The p-value =
`P(z\leq0.85)=0.8023374\approx0.8023`

Hence, the required probability : 0.8023