Question

There are 250 dogs at a dog show that weight an average of 12 pounds, with a standard deviation of 8 pounds .If 4 dogs are chosen at random, what is the probability that the average weight is greater then 8 pounds

Answer 1

Let X be a random variable representing the average weight of 4 dogs, then X ~ $N(12, {\frac {8^2} 4})$

$P(X>8)=P(N(12,{\frac {8^2} 4})>8)=P(12+4N(0,1)>8)=P(N(0,1)>-1)=0.84134$