Question

The size of fish is important to commercial fishing. A study conducted in 2102 found that the length of Atlantic cod caught in nets in Karlskrona, Sweden is normally distributed with mean 47 cm and standard deviation 3.9 cm. Source: Condition indices of Atlantic cod (Gadus morhua) biased by capturing method. M. Ovegard, K. Berndt, and S. Lunneryd, ICES Journal of Marine Science, August 21, 2012. 1. What is the probability that a randomly Atlantic cod is between 44 and 49 cm? Round your answer to 4 decimal places. 2. What is the probability that a random sample of 7 Atlantic cod have an average length between 44 and 49 cm? Enter your answer rounded to 4 decimal places and document how you obtained it in the space provided below.

Answer 1

Date : Griven : u=47 ; T: 3.9 (1) P(445x549) p(41 (44-47 3.9 474 49-47 3.9 . P(-0.77 < 2 < 0.51) = P(Z < 0.51) - P(Z < -0.77) 0.6950 O. 2206 Z=-0.77 Z-0.51 0.4744 (from 2-table) (2) PC445 x 49) - 44-47 x-M olun 49- 47 3.9/ - 3.9/17 VI) P(-2<z < 1:33) 1) P(Z < 1.33) - P(Z <-2) O. 9082 0.0228 (from Z-table 2=-2 0 Z=1.33 0 8854