Find the Value of a Normal Random Variable
-A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Between what times do we expect most (approximately 95%) of the boys to run the mile
A) between 322.4 and 557.6 sec
B) between 341.3 and 538.736 sec
C) between 345 and 535 sec
D) between 0 and 538.736 sec

Question

Quizplus · Accepted Answer

The 95% interval for a normal distribution is given by the mean plus or minus two standard deviations. Calculating this for the given mean (440) and standard deviation (60) gives: 440 ± 2(60) = 440 ± 120 = 320 and 560. So, the times between which we expect approximately 95% of the boys to run the mile are 320 seconds and 560 seconds. Option A, between 322.4 and 557.6 seconds, is the closest to this calculated range.