Respuesta :
The interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.
What is empirical rule?
According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
Here we had where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex].
When Ryan runs the 400 meter dash, his finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 0.5 seconds.
The interval of times that represents the middle 68% of his finishing times in the 400 meter race is,
[tex]P(75 - 0.5 < X < 75 + 0.5) = 68\%\\P(74.5 < X < 75.5) = 68\%[/tex]
Thus. the interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.
Learn more about empirical rule here:
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