Solutions for Session 2, Part B

See solutions for Problems: B1 | B2 | B3 | B4 | B5 | B6| B7| B8

 Problem B1 There are many possible answers. For example, we can be fairly confident that a box of Brand X raisins will have between 25 and 31 raisins.

 Problem B2 We can be almost certain that a new box of Brand Y raisins will have 28 raisins.

 Problem B3 Yes, the data strongly suggests that the next box will have 28 raisins, but it does not prove this. We would need to be sure that all boxes would have 28 raisins, not just our sample of 17 boxes. Statistically, there is no way to guarantee that the next box must have 28 raisins without sampling all boxes or without knowing something about the process involved in packaging Brand Y raisins. This is true regardless of how many boxes we sample; it only becomes more and more likely that the next box will have 28 raisins.

 Problem B4 We can still be fairly confident that a box of Brand X raisins will have between 25 and 31 raisins. In looking at the variation, though, it is quite likely that a box of Brand X raisins will have between 27 and 29 raisins. Still, no single number can describe our expectation for the number of raisins in a box of Brand X raisins.

 Problem B5 The range of possible data values is between 25 and 31 raisins, so the horizontal axis will include each number from 25 to 31: It would not matter if, for example, there were no values of 30 in the data set. All values in the range of possible data values must be included in the line plot, just as all numbers are indicated on a number line even though some of them may not be included in a list.

Problem B6

 a. The minimum raisin count is the leftmost dot, which indicates 25 raisins. b. The maximum raisin count is the rightmost dot, which indicates 31 raisins. c. Counting the dots tells us that a total of 10 boxes contain between 26 and 28 raisins. d. All 17 boxes do. e. The most frequent count is the tallest stack of dots, 28 raisins. There are five boxes with this frequency. f. Two boxes contain more than 29 raisins. g. Fifteen boxes contain 29 or fewer raisins. h. One box contains fewer than 26 raisins. i. One box contains 25 or fewer raisins. j. Fourteen boxes contain between 26 and 29 raisins.

 Problem B7 For Problem B6 (f) and (g), if you already know how many boxes contain more than 29 raisins, all other boxes must contain 29 or fewer raisins. Instead of counting a large number of boxes for Problem B6 (g), you could subtract the answer to Problem B6 (f), which is 2, from the total number of boxes, 17, to get your answer, 15. As for Problem B6 (h) and (i), they are identical questions because the data is discrete. There is no way to have between 25 and 26 raisins, so asking how many boxes have fewer than 26 raisins is the same as asking how many have 25 or fewer.

Problem B8

 a. The box of raisins should have between 25 and 31 raisins. b. The box of raisins is very likely to have between 26 and 29 raisins. c. The box of raisins is unlikely to have 28 raisins, but this is the most likely number from our sample.