Answer to Question #201728 in Statistics and Probability for Gregorio Dagun

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 greater than 8 pounds?

Answer 1

$\mu=12 \\ \sigma=8 \\ n=4 \\ P(\bar{X}>8) = 1 -P(\bar{X}<8) \\ = 1 -P(Z< \frac{8-12}{8 / \sqrt{4}}) \\ = 1 -P(Z < -1) \\ = 1 -0.1586 \\ = 0.8414$