Question

The U.S. Fish and Wildlife Service reported that 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 percent of six-year-old rainbow trout are between 400 and 500 millimeters long? Round your answer to four decimal places.

Option 1: 0.7881
Option 2: 0.7267
Option 3: 0.8994
Option 4: 0.6103

Answer 1

To find the percent of six-year-old rainbow trout between 400 and 500 millimeters long, calculate the z-scores and use the standard normal distribution table.

Step-by-step explanation:

To find the percent of six-year-old rainbow trout that are between 400 and 500 millimeters long, we need to calculate the z-scores for both values and use the standard normal distribution table. The formula to calculate the z-score is (x - mean) / standard deviation. For 400 millimeters, the z-score is (400 - 481) / 41 = -1.976. For 500 millimeters, the z-score is (500 - 481) / 41 = 0.463. Now, we can use the standard normal distribution table to find the area between these two z-scores.

Looking up the z-scores in the table, we find that the area to the left of -1.976 is 0.0251 and the area to the left of 0.463 is 0.6784. To find the area between these two z-scores, we subtract the smaller area from the larger area: 0.6784 - 0.0251 = 0.6533.

So, the percent of six-year-old rainbow trout between 400 and 500 millimeters long is 65.33% (rounded to four decimal places). Therefore, the correct option is Option 4: 0.6103.