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.
1 answer:
Answer:
99.7%
Step-by-step explanation:
Given that mean (μ) = 394.3 ms and standard deviation (σ) = 84.6 ms.
The empirical rule states that for a normal distribution:
68% falls within one standard deviation (μ ± σ) 95% falls within two standard deviation (μ ± 2σ) 99.7% falls within three standard deviation (μ ± 3σ) one standard deviation = 394.3 ± 84.6 = (309.7, 478.9). 68% falls within 309.7 and 478.9 ms
two standard deviation = 394.3 ± 2 × 84.6 = (225.1, 563.5). 95% falls within 225.1 and 563.5 ms
three standard deviation = 394.3 ± 3 × 84.6 = (140.5, 648.1). 99.7% falls within 140.5 and 648.1 ms
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