Question

the example for 5.31 is also attached

5.33 Can volumes. Averages are less variable than individual observations. It is reasonable to assume that the can volumes in Exercise 5.31 vary according toa Normal distribution. In that case, the mean x of an SRS of cans also has a Normal distribution (a) Make a sketch of the Normal curve for a single can. Add the Normal curve for the mean of an SRS of five cans on the same sketch. (b) What is the probability that the volume of a single randomly chosen can differs from the target value by 0.1 ml or more? (c) What is the probability that the mean volume of an SRS of five cans differs from the target value by 0.1 ml or more?

Answer 1

5.33(a)random variable denoting amount of energy drink in a can N(250, (0.4)2) mean amount of energy drink in 5 cans~N (250, (0.4)/5) random variable denoting amount oj energy r

(b) Plı-250| > 0.1) = 1-Plı-250| < 0.1) = 1-(20(0.25)-1) = 2(1-9(0.25)) = 0.8026. /5 (c) P(F-25이 > 0.1) = 1-PlF-250 < 0.1) = 1-1 2D(-)-1 2(1-Φ(v/5/4)) = 0.5762