7. A factory is producing packs of potato chips using two machines, A and B, only. It is known that the weights of the packs of potato chips produced by machine A follow a normal distribution of mean 79.8 g and standard deviation 0.6 g, while the weights of the packs of potato chips produced by machine B follow a normal distribution of mean 80.1 g and standard deviation 0.5 g. It is known that about 42% of the packs of potato chips produced by this factory weigh less than 79.9 g. (a) A pack of potato chips is randomly chosen from the outputs of machine A. Find the probability that it weighs less than 79.9 g. (b) A pack of potato chips is randomly chosen from the outputs of machine B. Find the probability that it weighs less than 79.9 g. (c) A pack of potato chips is randomly chosen from the outputs of this factory and is found to weigh less than 79.9 g. Find the probability that it was produced by machine A.

4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st

4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min

Suppose that heights of 10-year-old boys in the US vary according to a normal distribution with mean of 138 cm and standard deviation of 7. Compute the Z-score for a boy with height of 150 cm and find the correct interpretations.   a. Boy's height is 0.71 standard deviation lower the national average   b. Boy's height is 1.71 standard deviation above the national average   c. Boy's height is 1.71 standard deviation lower than the national average   d. Boy's height is 2.71 standard deviation above the national average

Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 8vmillion dollars and a standard deviation of 1.1million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 15%of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.