SOLUTION: 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 dis

Question 1169546: 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 460 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 345 seconds.

.5107

.0107

.9893

.4893

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability is .0107

i used the ti-84 plus calculaor.

there are several online calculators you can use that will provide the same answer to you.

one of the calculators that i use can be found at https://www.calculator.net/z-score-calculator.html?c1raw=-2.3&c1mean=0&c1sd=1&calctype=zscore&x=66&y=25

the calculator can work off of z-scores or off of raw scores.

put in a mean of 460 and a standard deviation of 50 and a raw score of 345.
hit calculate and your answer shows up.

here's what it shows.

the calculator tells you what the z-score is (-2.3)

you can calculate the z-score yourself by using the formula of:
z-score = (x-m)/s
x is the raw score
m is the mean
s is the standard deviation.
in your problem (x-m)/s becomes (345-460)/50 = -2.3

if you are using the z-score rather than the raw score, you would enter a mean of 0 and a standard deviation of 1 and give it the z-score instead of the raw score.

you would get the following results.

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