CAHSEE practice: Problems 17-19

Problem 17: Michelle read a book review and predicted that the number of girls who will like the book will be more than twice the number of boys who will like the book. So, she predicted that the girls would be more than twice -- let me box it out -- more than twice the number of boys who will like the book. Which table shows data that supports her prediction? So essentially, we just need to find one of the tables where the number of girls who like the book, that's just this column right here -- the number who like the book -- should be more than twice the number of boys. Let's see the girls here is 40, the boys here are 35, there are more girls than boys, but it's not more than twice the boys. The boys are 35. Twice the boys would be 70, and girls is definitely not more than 70, so that's not our answer. Let's just go here, well, here the boys are more than the girls, which definitely isn't going to be the case. We need a situation where the girls are more than twice the number of boys. So that's not our situation, because the girls are actually smaller than the boys here. Here we have 35 boys, if you multiply that by 2, you would get 70 boys. So twice the boys is 70. And we see that the girls, at 80, are more than twice the boys at 70. So that is our choice. The girls are more than twice the boys. And if you look here, the boys and girls are even, so the girls are definitely not more than twice the boys. So we know definitely, that B is our answer. Go to the next page, Problem 18: Anna has the letter tiles below in a bag. It's very interesting, it just happens to spell out statistics. She reached in the bag, and pulled out an S. She then put the tile back in the bag. OK, so all of them are still in the bag. If Anna randomly selects a tile from the bag, what is the probability she will select an S again? So this is a trick question on some level, because this first part, that she reached in the bag and pulled out an S and she then put the tile back in the bag. That doesn't do anything! The fact that she pulled out an S, and then put it back in the bag, that shouldn't change what happens afterward. If she took out the S and kept the S out, then this would be a different type of problem. But since she took out the S and put it back in, this is almost useless information. We still have all of these letters in the bag. It says if Anna randomly selects a tile from the bag, what is the probability she'll select an S? So all we have to say is, all of these are in the bag, so what are the possible outcomes? So there's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 possible outcomes. 10 possible outcomes, so that's going to be the denominator for our probability. And then, what are the outcomes that satisfy our conditions? Or, what are the outcomes where she selects an S? She selects an S, so there's 1 S, 2 S, and 3 S's. There's 3 out of the 10 situations involve selecting an S, so the answer is 3/10. And the reason why I said it's a trick question, is because they write statement which really doesn't change the problem it all. She took out an S, she put it back. If she said that she took out an S, and then she did not put it back in the bag, then you would say, oh gee, then there's only 9 tiles left; and only two of them are S's, and then you would have said 2/9. But since she did put the S back in the bag, we could say, oh, there's 10 letters in the bag, 3 of them are S's, so the answer is 3/10. Problem 19: The scatterplot below shows the ages of some children and the distance each lives from school. So this is the ages, and then this is the distance in that axis. Which statement best describes the relation between age and distance from the school? Just looking at this, I really don't see any relation, it seems to be fairly random. Let's see what the statements tell us. As age and increases, the distance from school increases. No, not really, I mean, that would look something like this. So this is our age axis, this is our distance axis, what A is describing is as age increases, the distance from school increases. The data points should look something like this. They should generally increase -- distance should generally increase as age increases. That's not what we see here, I mean this really kind of seems arbitrary. It's not like this nice upward trend. B, as age increases the distance from school decreases. Well I don't even see a downward trend either, what B is describing, the data would look like this. Where we have this downward trend. I don't see that here, either. C, as age increases, the distance from school remains constant. What C is describing would have data that looks like this. That regardless of age, the distance from school is about the same. I don't really see that either. There's still a huge spread of distances. And then D, there is no relationship between the age and distance from school. I'll go with that one because, you could imagine, if I tried to draw trend line, I could draw something like that, maybe that makes it look like there's a trend. But I just as easily could have drawn that. And looks just is good to me. Or I just as easily could have drawn that. None of these look like it fits the data any better. So, at least the answer that I feel comfortable with is D.