Answer to Question #190637 in Statistics and Probability for Ellyza jane

Question

There are 250 dogs at a dog show that weigh 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 greatee that 8 pounds

Answer 1

Solution:

Given, $\mu=12,\sigma=8,n=4$

$X\sim N(\mu,\sigma)$

$P(X>8)=P(z>\dfrac{8-12}{8/\sqrt{4}})=P(z>-1) \\=1-P(z\le-1)=1-[1-P(z\le1)] \\=P(z\le1)=0.84134$