Question

1) The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a 1). standard deviation of 9. If 9 fish are randomly selected, draw, label and shade the normal curve, find the z-scores, and find the probability that the mean weight will be between 17.6 and 23.6 lb. Draw, label, and shade: Z-scores: P(17.6<x< 23.6)

Answer 1

let x be a Nomally distributed random variable, with u= 20, SD = 9. Sample size n = 9. P(17.6< X<23.6) =P(176-20 < 24 < 23.6-20) =P(-0.21 <= 20.4) = P(Z <0-4)-Plz<-0-27) Plz <0-4)-1+P(Z <0.27) -0.6554 -1 +0.6054 = 0.2608 17.6 u=20 23.6 2 x-ll olin 23.6-20 9 kn Using Chebycher's inequality, P(1762x<23-6) = POR EN = P(0.8<2<12) = P(Z<1-2)-PL2<-08) = P(Z<1-27-1+P(Z <0.8) -0-8849-1+0.7881 = 0.613.