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%
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)
The mean length of six-year-old rainbow trout in an Alaskan river is 481 millimeters (mm) and...
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