Question

the times to complete an obstacle course is normally distributed with the mean of 73 seconds and standard deviation 9 seconds. What is the probability using the empirical rule that a randomly selected finishing time is less than 100 seconds

Answer 1

The probability of a finishing time being less than 100 seconds is approximately 99.7%, using the empirical rule for a normally distributed set of times with a mean of 73 seconds and a standard deviation of 9 seconds.

Step-by-step explanation:

Using the empirical rule (also known as the 68-95-99.7 rule), we can determine the probability that a finishing time is less than 100 seconds for an obstacle course where the mean time is 73 seconds with a standard deviation of 9 seconds. The empirical rule states that approximately 68% of data within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Calculating the number of standard deviations that 100 seconds is away from the mean:

(100 seconds - 73 seconds) / 9 seconds per standard deviation = 3 standard deviations

Since 100 seconds is three standard deviations away, we can say that the probability of a randomly selected finishing time being less than 100 seconds is approximately 99.7%.