Question

Adult walleye have a length with a mean of 44 cm and a standard deviation of 4 cm, and the distribution of lengths is approximately normal. what fraction of fish are greater than 41 cm in length?

Answer 1

Mean, mu=44 cm
standard deviation, sigma = 4 cm
X=41

We calculate the Z-value for 41 cm
Z(41)=(41-mu)/sigma=(41-44)/4=-0.75

The probability that x>X
P(x>X)
=P(x>41)
=1-P(x<41)
=1-0.2266274 (from standard normal distribution tables for left-tail of Z=-0.75)
= 0.7733726