A data scientist tracked how many cups of coffee she drank every day at work over the course of a year. She used the data to build a probability distribution where the random variable CCC represents the number of cups of coffee she drank on a given day. Here is the distribution:

C=\# \text{ of cups}C=# of cups 000 111 222 333

P(C)P(C)P, left parenthesis, C, right parenthesis 0.050.050, point, 05 0.100.100, point, 10 0.750.750, point, 75 0.100.100, point, 10

Calculate the mean of CCC.

An episode of a television show is 60 minutes long when it originally airs with commercials. on a dvd without commercials, the episode is only 417 minutes long. how many1-minute commercials did the episode include when it originally aired? write and solve an equation to justify your answer.

Marcus and cody both leave the park at the same time, but in opposite directions. if cody travels 6 mph faster than marcus and after 4 hours they are 64 miles apart, how fast is each traveling? solve using rare times time = distance.

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.