Question

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.
Round your answer to the nearest tenth.

Answer 1

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:

1. 68% falls within one standard deviation (μ ± σ)
2. 95% falls within two standard deviation (μ ± 2σ)
3. 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