Question

A normal distribution is observed from the times to complete an obstacle course. The mean 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 87 seconds?

Answer 1

To determine the probability of a finish time greater than 87 seconds, we apply the Empirical Rule and find it equates to 3 standard deviations above mean, resulting in a probability of 0.15%.

Step-by-step explanation:

The question revolves around the use of the Empirical Rule to determine the probability in a normal distribution. The mean time to complete an obstacle course is given as 69 seconds with a standard deviation of 6 seconds. According to the Empirical Rule:

To find out the probability of a finishing time being greater than 87 seconds, we first determine how many standard deviations above the mean this is:

(87 - 69) / 6 = 3

This indicates that 87 seconds is 3 standard deviations above the mean. Using the Empirical Rule, if 99.7% of the data falls within three standard deviations, this would leave 0.3% (or 0.003 in decimal form) of the data outside, which would be the tails of the distribution (both ends combined). Since we are looking for the area above 87 seconds, we only consider one tail, hence, we divide the 0.3% equally for each tail to get 0.15% (or 0.0015 in decimal form) for the probability that a randomly selected finish time is greater than 87 seconds.

Answer 2

P ( z > 87 ) < 0,0015

P ( z > 87 ) < 0,15 %

Step-by-step explanation:

Applying the simple rule that:

μ ± 3σ , means that between

μ - 9 = 60 and

μ + 9 = 78

We will find 99,7 of the values

And given that z(s) = 87 > 78 (the upper limit of the above mention interval ) we must conclude that the probability of find a value greater than 87 is smaller than 0.0015 ( 0r 0,15 %)