The time that it takes an Olympic runner to finish the 100-meter dash is approximately normal with a mean of 9.83 seconds with a standard deviation of 0.06 seconds. What is the probability it would take The runner less than 10.01 seconds to finish the race? Give your answer as a percentage.
A) 0.15%
B) 95%
C) 99.7%
D) 99.85%
E) None of the above.

Question

Quizplus · Accepted Answer

To find the probability, we first calculate the Z-score using the formula Z = (X - μ) / σ, where X is the value of interest (10.01 seconds), μ is the mean (9.83 seconds), and σ is the standard deviation (0.06 seconds). Plugging in the values, we get Z = (10.01 - 9.83) / 0.06 = 3. This Z-score corresponds to a probability of 99.85% when looking up in a standard normal distribution table or using a calculator, indicating the probability of a runner finishing in less than 10.01 seconds.

The Time That It Takes an Olympic Runner to Finish