Eggs The ISA Babcock Company supplies poultry farmers with h

Eggs The ISA Babcock Company supplies poultry farmers with hens, advertising that a mature B300 Layer produces eggs with a mean weight of 60.7 grams. Suppose that egg weights follow a Normal model with standard deviation 3.1 grams. a) What fraction of the eggs produced by these hens weigh more than 62 grams? b) What?s the probability that a dozen randomly selected eggs average more than 62 grams? c) Using the 68-95-99.7 Rule, sketch a model of the total weights of a dozen eggs.

Solution

a)

z value for 62, z= (62-60.7)/3.1 =0.42

p(x>62) = p(z>0.42) =0.3372

b)

for n=12, standard error= 3.1/sqrt(12) =0.8949

z=(62-60.7)/0.8949=1.45

p(meanx>62) = p(z>1.45) = 0.0735

c)

total weight of dozen eggs = 12*60.7=728.4

sd of total =12*3.1=37.2

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