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satela [25.4K]
3 years ago
10

Race times at the local monthly 5k run are normally distributed, with a mean time of 32 minutes and a standard deviation of 4 mi

nutes. Using the empirical rule, approximately what percent of racers cross the finish line between 28 and 36 minutes? 32% 68% 95% 99.7%
Mathematics
1 answer:
galina1969 [7]3 years ago
7 0

Answer:

68%

Step-by-step explanation:

The mean is 32 minutes, and the standard deviation is 4 minutes.

28 is 1 standard deviation below the mean, and 36 is 1 standard deviation above the mean.

According to the empirical rule, 68% of a normal distribution is between -1 and 1 standard deviations.  95% is between -2 and 2 standard deviations.  99.5% is between -3 and 3 standard deviations.

So the answer is 68%.

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Answer:

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Step-by-step explanation:

Statement that is expressed in words

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Answer:

See proof below

Step-by-step explanation:

We will use properties of inequalities during the proof.

Let y\in (x-\epsilon,x+\epsilon). then we have that x-\epsilon. Hence, it makes sense to define the positive number delta as \delta=\min\{x+\epsilon-y,y-(x-\epsilon)\} (the inequality guarantees that these numbers are positive).

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Step-by-step explanation:

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