14 April, 09:41

# A random sample of adult female reaction times has a sample mean of x¯=394.3 milliseconds and sample standard deviation of s=84.6 milliseconds. Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

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Answers (1)
1. 14 April, 10:22
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The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 394.3 ms

Standard deviation = 84.6 ms

Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

140.5 = 394.3 - 3*84.6

So 140.5 is 3 standard deviations below the mean.

648.1 = 394.3 + 3*84.6

So 648.1 is 3 standard deviations above the mean.

By the Empirical Rule,

The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.
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