Find the Value of a Normal Random Variable
-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 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
A) $386 \mathrm { sec }$
B) $514 \mathrm { sec }$
C) $532.25 \mathrm { sec }$
D) $367.75 \mathrm { sec }$

Question

Find the Value of a Normal Random Variable
-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 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 
A) $386 \mathrm { sec }$
B) $514 \mathrm { sec }$
C) $532.25 \mathrm { sec }$
D) $367.75 \mathrm { sec }$

Quizplus · Accepted Answer

To find the time that corresponds to the fastest 10%, we need to find the 10th percentile of the normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Using the z-table, the z-score for the 10th percentile is approximately -1.28. Using the formula $X = \mu + z\sigma$, we calculate $X = 450 + (-1.28)(50) = 386$ seconds.

Find the Value of a Normal Random Variable -A Physical 386sec386 \mathrm { sec }386sec

Find the Value of a Normal Random Variable
-A Physical $386 \mathrm { sec }$