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When Ryan runs the 400 meter dash, his finishing times are normally distributedwith a mean of 65 seconds and a standard deviation of 2 seconds. If Ryan were to run.36 practice trials of the 400 meter dash, how many of those trials would be between63 and 65 seconds, to the nearest whole number?

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Solution

Step 1

Dalvin's finishing time is normally distributed with a mean of 65 seconds and a standard deviation of 1 second.

[tex]\begin{gathered} \text{Mean }\mu\text{ = 65} \\ Standard\text{ deviation }\sigma\text{ = 1} \end{gathered}[/tex]

Step 2

Under the empirical rule, 68% of the results will be within 1 standard deviation.

Step 3

Since the standard deviation is 1 second, 68% of Dalvin's finishing time will be between 63 and 65 seconds.

Final answer

68%

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