Problem
When Salma runs the 400 meter dash, her finishing times are normally distributed with a mean of 70 seconds and a standard deviation of 0.5 seconds. If Salma were to run 39 practice trials of the 400 meter dash, how many of those trials would be faster than 71 seconds, to the nearest whole number?
Solution
Step 1 ：Find the z-score for 71 seconds: \( z = \frac{x - \mu}{\sigma} = \frac{71 - 70}{0.5} \)
Step 2 ：Calculate the z-score: \( z = 2 \)
Step 3 ：Find the probability using z-table: \( P(z < 2) = 0.9772 \)
Step 4 ：Multiply the probability by the number of trials: \( 39 * 0.9772 \)
Step 5 ：Round the result to the nearest whole number: \( 38 \)
