Aquality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. not every bag contains exactly the same weight. but if more than 15% of bags are over-filled then they stop production to fix the machine. they define overfilled to be more than 1 ounce above the weight on the package. the engineer weighs 100 bags and finds that 21 of them are over-filled. he plans to test the hypotheses h 0: p = 0.15 versus h a: p > 0.15. what is the test statistic? group of answer choices z = − 1.47 z = − 1.47 z = − 1.47 z = − 1.47 z = 4 z = 4 z = 4 z = 4 z = 1.68 z = 1.68 z = 1.68 z = 1.68

He ! a group of farmers planned to clean 80 acres of wheat per day to finish the work on schedule. right before the work started, they received a new piece of machinery that them clean 10 more acres per day than originally planned. as a result of increased productivity in the last day before the deadline they only had to clean 30 acres. how many acres of wheat did the group of farmers have to clean?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

The data set represents the ages of players in a chess club. 27, 34, 38, 16, 22, 45, 54, 60. what is the mean absolute deviation of the data set?