Question

Fish story: According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 478 millimeters with a standard deviation of 38 millimeters. Assume these lengths are normally distributed. Round the answers to at least two decimal places. (a) Find the 54th percentile of the lengths.

Answer 1

Answer:

11.29.

Step-by-step explanation:

We are given that The mean length of six-year-old rainbow trout in the Arolik River in Alaska is 478 millimeters with a standard deviation of 38 millimeters.

We are also given that these lengths are normally distributed.

So, The highest value is at mean .(Refer the attached figure).

Formula : $Percentile = \frac{Length}{Maximum} \times 100$

$54 = \frac{Length}{478} \times 100$

$\frac{5400}{478} =Length$

$11.297 =Length$

The 54th percentile of the lengths is 11.29.