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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 a standard deviation of 40 seconds. Between what times do we expect approximately 95% of the boys to run the mile?

Respuesta :

jmonterrozar

Answer:

Between 371.6 seconds or 528.4 seconds.

Step-by-step explanation:

Thanks to the normal distribution table (attached) we know that:

95% would be a z between -1.96 and +1.96

z = (x- m) / sd

where x is the value we want to calculate, m is the mean (450) and sd is the set deviation (40). Now, replacing we have:

+ -1.96 = (x-450) / 40

+ -78.4 = x-450

x = 450 + - 78.4

x1 = 528.4

x2 = 371.6

In other words, the result is between 371.6 seconds or 528.4 seconds.

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