Question

Assume that on average I can run 3 miles before my legs give out with a standard deviation of 0.6 miles. What is the probability that tomorrow I run less than 2.5 miles?

Answer 1

To find the probability of running less than 2.5 miles, calculate the z-score using the formula (x - mean) / standard deviation. Then, look up the z-score in a z-table or use a calculator to find the area to the left of the z-score.

Step-by-step explanation:

To find the probability that you run less than 2.5 miles tomorrow, you need to convert your running distance to a z-score. A z-score tells you how many standard deviations an observation is from the mean. You can calculate the z-score using the formula:
z = (x - mean) / standard deviation
Plugging in the values, we get:
z = (2.5 - 3) / 0.6 = -0.83
Now, you can look up the z-score in a z-table or use a calculator to find the area to the left of -0.83. The probability of running less than 2.5 miles is the area to the left of the z-score.