Place the events in order of increasing likelihood.
A. Landing on the number 33 on a spinner with 100 numbers.
B. Rolling a sum of 13 on a roll of two dice.
C. Drawing a black card from five decks of cards.
D. Drawing a red or black card from a deck.
Responses
A B < A < D < C
B D < C < A < B
C A < B < C < D
D B < A < C < D
A < B < D < C
You roll a six-sided die. How likely is it that you roll a number greater than 6?
Responses
A unlikely
B likely
C certain
D impossible
D (impossible)
Which THREE statements are correct when determining the likelihood of a chance event occurring?
Responses
A A probability of 12
means the event will more than likely occur.
B A chance event with a 0.95 probability of occurring is likely to occur
C A chance event with a 0.35 probability is more likely to occur than an event with a 0.40 probability.
D A chance event with a probability of 0.68 is more likely to occur than an event with a 0.55 probability.
E The closer the probability of a chance event is to 0, the less likely it is for the event to occur.
B, D, and E are correct.
Brad and Tom are comparing their classes' scores on a math test. Both of their classes had mean scores of 80 on the test, but Brad's class had a range of 6 while Tom's class had a range of 30. If the highest possible score was 100, which class had the LOWEST score in it?
Responses
A It cannot be determined from the information.
B Brad's class had the lowest score in it.
C Tom's class had the lowest score in it.
D The lowest score occurred in both classes
C (Tom's class had the lowest score in it).
If both classes had a mean of 80, this means that the total points earned by each class was the same. However, Tom's class had a greater range, which means that there must be more points concentrated toward the upper end of the range. This means that Tom's class likely had a low score that was lower than the low score in Brad's class.
Julie conducts an experiment to find the average word length in a book for a 4th grader and a book for a 8th grader. She finds that for the fourth grade book the mean word length is 5 letters with a range of 6 and for the 8th grade book the mean word length is 6 letters with a range of 9. Which statement is true?
Responses
A The longest word in the 8th grade book contains 15 letters.
B The longest word in the book for the 4th grader is longer than that in the 8th grade book.
C On average, the book for the 8th grader has longer words.
D The word length varies more in the 4th grade book than the 8th grade book.
A (The longest word in the 8th grade book contains 15 letters) is true based on the information given.
We are told that the range of word length in the 8th grade book is 9, so the highest possible word length is 6 + 9 = 15. There is no information given about the longest word in the 4th grade book, so we cannot determine if statement B is true. Statement C is true based on the given means. Statement D is true based on the given ranges.
At a pet store, the lizards in aquarium A have a mean length of 13 cm and a range from 9 cm to 15 cm. In aquarium B, the lizards have a mean length of 15 cm and a range from 14 cm to 17 cm. Which statement BEST compares the lizards in the two aquariums?
Responses
A On average, the lizards in aquarium A are longer.
B The lizards in aquarium A vary in length more than aquarium B.
C Aquarium A has the longest lizard at this pet store.
D The lizards in aquarium B vary in length more than aquarium A.
B (The lizards in aquarium A vary in length more than aquarium B) is the best statement that compares the lizards in the two aquariums.
While the mean length of lizards in aquarium B is longer than that in aquarium A, we know that the range of length in aquarium B is only 3 cm, which means that there is not much variation in lizard length. In comparison, the range in aquarium A is 6 cm, which means there is a greater variation in lizard length. Therefore, statement B is the best comparison. Statement A is not true, as the mean length in aquarium B is longer. Statement C cannot be determined based on the given information, and statement D is not true based on the given ranges.
At a pet store, the lizards in aquarium A have a mean length of 13 cm and vary from 9 cm to 15 cm. In aquarium B, the lizards have a mean length of 15 cm and vary from 14 cm to 17 cm. Which statement BEST compares the lizards in the two aquariums?
Responses
A On average, the lizards in aquarium B are longer than the lizards in aquarium A.
B The lizards in aquarium B vary in length more than the lizards in aquarium A.
C Half of the lizards in aquarium A are 14 cm to 15 cm long.
D There are more lizards in aquarium A than in aquarium B.
A (On average, the lizards in aquarium B are longer than the lizards in aquarium A) is the best statement that compares the lizards in the two aquariums.
We are told that the mean length in aquarium B is longer than that in aquarium A, meaning that the lizards in aquarium B are, on average, longer than those in aquarium A. Statement B is not true, as we are told that the range in aquarium B is only 3 cm, while the range in aquarium A is 6 cm. Statement C cannot be determined based on the given information, and statement D cannot be determined based on the given information.
A group of middle school boys have a mean height of 167 cm and vary from 164 cm to 169 cm. A group of high school boys have a mean height of 180 cm and vary from 175 cm to 183 cm. Which statement BEST compares the two groups of boys?
Responses
A For these groups, every high school boy is taller than every middle school boy.
B Half of the high school boys are between 181 cm and 183 cm in height.
C The middle school boys vary in height more than the high school boys.
D On average, the middle school boys are taller.
C (The middle school boys vary in height more than the high school boys) is the best statement that compares the two groups of boys.
Although the mean height of the high school boys is higher than that of the middle school boys, this does not mean every high school boy is taller than every middle school boy, so statement A is not true. Statement B cannot be determined based on the given information. We are told that the range of height among middle school boys is 5 cm (from 164 cm to 169 cm), while the range of height among high school boys is only 8 cm (from 175 cm to 183 cm), so statement C is true. Statement D is not true, as we are told that the mean height of the high school boys is higher than that of the middle school boys.