Question

The mean length of six-year-old rainbow trout in an Alaskan river is 481 millimeters (mm) and the standard deviation is 41 mm. Assuming the population is normally distributed, what is the probability that a randomly selected six-year-old rainbow trout has length between 460 mm and 500 mm? a) 30.4% b) 37.4% c) 49.7% d) 56.7% e) 67.8%

Answer 1

Solution :

Given that ,

mean = = 481

standard deviation = = 41

P(460 < x < 500) = P[(460 - 481)/ 41) < (x - ) /  < (500 - 481) / 41) ]

= P(-0.5122 < z < 0.4634)

= P(z < 0.4634) - P(z < -0.5122)

= 0.6785 - 0.3043

= 0.3742

Probability = 37.4%

option b)