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

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Question 1188939: 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. The fitness association wants to recognize the boys whose times are among the top (or fastest) 10% with certificates of recognition. What time (in seconds) would the boys need to beat in order to earn a certificate of recognition from the fitness association? Round your answer to one decimal place.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the population mean is 440 seconds.
the population standard deviation is 60 seconds.
the z-score that has 10% of the area under the normal distribution curve to the left of it is equal to -1.28155 rounded to 5 decimal places.
the raw score associated with that is based on the z-score formula of:
z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
the formula becomes:
-1.28155 = (x - 440) / 60
solve for x to get:
x = -1.28155 * 60 + 440 = 363.107 seconds
any times less than that will get the certificate of recognition.