An operation manager at a pump manufacture wants to test their pump outputs. The design engineer claims they have a mean output of 272 watts with a variance of 144. What is the probability that the mean pump output would be greater than 271.4 watts in a sample of 100 pumps if the claim is true?

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.