Question

1. You’re going to catch a fish in the river. You know that its size is normally distributed with mean 56 inches and standard deviation 7 inches. What is the probability that you catch a fish over 60 inches? What is the probability that you catch a fish less than 50 inche

Answer 1

$Given \; that, μ=56, σ=7,then,\\ a) P(x>60) = P( Z >\frac{60-56}{7})\\ =P(Z>0.57)\\= 0.5-P(0<Z<0.57)\\ =0.5-0.2157=0.2843\\ b) P(x<50) = P( Z <\frac{50-56}{7})\\ =P(Z<-0.86)\\= 0.5-P(0<Z<0.86)\\ =0.5-0.3051=0.1949\\$