Kilometer Run

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.

Height

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.

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
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.