A recently discovered dietary additive for chicken feed has been shown to result
ID: 3277151 • Letter: A
Question
A recently discovered dietary additive for chicken feed has been shown to result in eggs with slightly hardened shells. However, the eggs are also somewhat heavier than typical eggs, causing packagers concern that egg cartoons (holding a dozen eggs each) may be prone to bursting.
(a) If the weight of hard-shelled eggs is normally distributed with a mean of 2.5 ounces and a standard deviation of 0.12 ounce, and the bursting strength of existing cartons is normally distributed with a mean of 32.4 ounces and standard deviation of 0.66 ounce, what proportion of the cartons will burst when filled with hard-shelled eggs?
(b) If a grover orders one-hundred cartons of hard-shelled eggs, what is the probability that at least one carton will burst from the weight of the eggs?
Explanation / Answer
a) here mean weight of one dozen cartons X=12*2.5=30
and mean of bursting strength of existing cartons Y=32.4
also std error of mean difference =(12*0.122+0.662)1/2 =0.78
hence proportion of the cartons will burst when filled with hard-shelled eggs=P(X-Y>0)
=P(Z>(32.4-30)/0.78)=P(Z>3.0769)=0.001046
b)probability that at least one carton will burst from the weight of the eggs =1-P(none of 100 will go burst)
=1-(1-0.001046)100 =0.0993