A physical fitness association is including the mile run in its secondary-school

Question

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 450 seconds and standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. a What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? b. Between what times do we expect most (the middle 95%) of the boys to run the mile?

Explanation / Answer

a) for fastest 10% ; critical z= -1.2816

therefore corresponding time =mean +z*std deviaiton =450-1.28*40= 398.7 seconds

b) for 95% CI ; z=-/+ 1.96

therefore corresponding values =mean -/+ z*std deviaiton =450 -/+ 1.96*40=371.6 ; 528.4

therefore the time should be between 371.6 seconds to 528.4 seconds

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