Question

a normal distribution is observed from the times to complete an extreme ninja obstacle course. the mean time is 69 seconds and the standard deviation is 6 seconds. using the empirical rule, what is the probability that a randomly selected finishing time is greater than 75 seconds? provide the final answer as a percent rounded to two decimal places.

Answer 1

Using the Empirical Rule and normal distribution, the probability that a randomly selected finishing time is greater than 75 seconds is 16%, as 68% of data falls within one standard deviation, and 75 seconds is exactly one standard deviation above the mean.

Step-by-step explanation:

To calculate the probability that a randomly selected finishing time is greater than 75 seconds, we need to use the Empirical Rule and normal distribution properties. The Empirical Rule states that for a normal distribution:

• 68% of data falls within one standard deviation of the mean.
• 95% of data falls within two standard deviations of the mean.
• 99.7% of data falls within three standard deviations of the mean.

In this case, our mean (μ) is 69 seconds, and the standard deviation (σ) is 6 seconds.

To find the probability greater than 75 seconds, we calculate how many standard deviations above the mean this is: (75 - 69) / 6 = 1. This means that 75 seconds is one standard deviation above the mean.

Since 68% of data falls within one standard deviation either side of the mean, we have (100% - 68%) / 2 = 16% of data lying beyond one standard deviation above the mean.

Therefore, the probability that a randomly selected finishing time is greater than 75 seconds is 16%.