Find and Interpret the Area under a Normal Curve
-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 470 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 378 seconds to run the mile.
A) 0.9893
B) 0.4893
C) 0.0107
D) 0.5107

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected boy will take longer than 378 seconds, we first calculate the Z-score for 378 seconds using the formula Z = (X - μ) / σ, where X is 378, μ (mean) is 470, and σ (standard deviation) is 40. This gives Z = (378 - 470) / 40 = -92 / 40 = -2.3. Looking up the Z-score of -2.3 in the standard normal distribution table or using a calculator, we find the area to the left of this Z-score is approximately 0.0107. Since we want the probability of taking longer than 378 seconds, we subtract this from 1 (1 - 0.0107) to get approximately 0.9893. This means there's a 98.93% chance a randomly selected boy will take longer than 378 seconds to run the mile.

Find and Interpret the Area Under a Normal Curve