Sample Examination One - La Jolla High School

Section {{
Part B
Time-25 minutes
Question 5
Percent of Section lI srade-25
Dinections: Shorv all your work. Indicate clearly the methoels vou use, because 5,ou *,ill
be graded on the correctness of vour method as rvell as on the accuracy clf ycur results
and explanations.
6" Two srvimmers have been training for a big race in the 100 meter backstroke. Their
times are knorvn to be normally distributed with the follorving distributions (in
seconds). We can also assuine thatthe times of the two swimmers are independent.
swimmer 1: mean = 76.76 standard deviation : 3.08
swimmer 2: mean = 77.9 standard deviation :2.49
(a) The srvimmers keep track of their progress over the season. What is the mean
and standard deviatior-r of the first sn,irnmer's time (x) minus the second
srl'immer's [v) time?
H'- r=
6*-)'=
(b) Using your results in part (a), what is the probability the second swimmer rvill
beat the first s*'immer on any given race? Round your answer to the nearest
hundredth. Please note that the lowest time q,ins a race.
or feusrn9 any
part of this page is illegal
28