The Huffingdale All Boys School has produced a comprehensive set of

The Huffingdale All Boys School has produced a comprehensive set of running standards for young boys. These standards are based on data from young boys attending Huffingdale in good health conditions - as determined by a physician. The table displays the percentile distribution of time on a kilometer run for Huffingdale students at grade levels 1 through 5 according to the Huffingdale model. In a model population -- a large population of young students grade 1 through 5 that conforms to the Huffingdale running standards -- for n=5, 15, 50, 85, and 95, the nth percentile in running time for a given grade is the unique running time among boys of that grade level that is slower than or equal to n percent, and faster than or equal to (100 - n) percent, of running times for students of that grade level.



The graph shows the percentile distribution of height, in centimeters, for running times from 500 to 700 seconds, according to the Huffingdale model. In a model population, for n=5, 15, 50, 85, and 95, the nth percentile in height for a given running time is the unique height among boys of that running time that is taller than or equal to n percent, and shorter than or equal to (100-n) percent, of heights of boys of that running time.



1. Consider an individual boy from a model population. Suppose that from grades 1 through 5, this boy's height is at the 50th percentile for his running time and his running time is at the 50th percentile for his grade level. Which one of the following statements must be true of the boy at Grade 5?

A. His grade level is at the 50th percentile for his running time.
B. His height is at the 50th percentile for his grade level.
C. His running time is at the 50th percentile for his height.
D. His height is approximately 130% of his height in Grade 2.
E. His height is approximately 185% of his height in Grade 2.



2. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

Yes	No	Statements
		If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.
		If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.
		If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.

3. A boy, John, selected at random from a model population runs a 10:50 kilometer. Another randomly selected boy, Peter, runs a 10:00 kilometer. Both boys measured 80cm tall. The difference in their percentiles in height among boys who run their respective speeds is most closest to

A. 15%
B. 25%
C. 30%
D. 35%
E. 40%



4. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

Yes	No	Statements
		If he is in the second grade or lower, the probability that his speed is slower than 11:00 is greater than 85%.
		If he runs at most a 9 minute kilometer (no faster), the probability that his height is less than 80cm is no greater than 50%.
		If he runs a 7:30 kilometer run, he is definitely in the 5th grade.

5. Joshua is a boy in the 3rd grade whose kilometer run time is 11:20 and whose height is 81cm. For each of the following statements, select Yes if, based on the given information, it must be true of Joshua relative to a model population. Otherwise, select No.

Yes	No	Statements
		Approximately 95% of boys at the same height are slower than Joshua.
		No more than 15% of boys at this grade level are slower than Joshua.
		Joshua's speed is faster than or equal to that of 50% of boys in the second grade.

6. Joshua is a boy in grade 4 whose running time is 10:30 and whose height is 80cm. For each of the following statements, select Yes if, based on the given information, it must be true of Joshua relative to a model population. Otherwise, select No.

Yes	No	Statements
		At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's.
		At least 80% of boys at this grade level have running times within 90 seconds of Joshua's running time.
		Joshua's running time is faster than that of at most 5% of boys in the fourth grade.