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3 of 5 3. A physical fitness association is including the mile run in its second

ID: 2922637 • Letter: 3

Question

3 of 5 3. A physical fitness association is including the mile run in its secondary-school fitmess 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. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? Vm Distribution of the Sample Mean If we are taking a random sample of sze n from a population with mean and standard deviation . then the mean R has mean and standard deviation . (The standard deviation of R is also known as the standard error of the mean.) If the populations is normally distributed, then the sample mean isX normally distributed, so z has a standard normal distribution. Even if the populations is not normally distributed, the Central Limit Theorem tell us that for large samples (a-30) the sample mean? is approximately nomally distributed, so approximately standard normal.

Explanation / Answer

Answer:

z value for top 10% = 1.282 ( from standard normal distribution).

x= mean+z*sd

=460+1.282*50

=524.1