Avoiding an accident while driving can depend on reaction time. Suppose that reaction time, measured from the time the driver first sees the danger until the driver gets his/her foot on the brake pedal, is approximately symmetric and mound-shaped with mean 1.9 seconds and standard deviation 0.12seconds. Use the 68-95-99.7 rule to answer the following questions.

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What percentage of drivers have a reaction time more than 2.14 seconds?

Standard deviation is a statistical measure that quantifies the amount of variability or dispersion in a dataset. It measures how spread out the values are from the mean (average) of the dataset. In other words, it provides an indication of the average distance between each data point and the mean.

The given mean is μ = 1.9 and standard deviation is σ = 0.12.

It is known that the reaction time is approximately symmetric and mound-shaped.

Suppose that the distribution follows normal distribution.

So, we need to find the percentage of drivers having a reaction time of more than 2.14 seconds.

The standardized value of x is:

z = (x - μ) / σ

Where x is the random variable, μ is the mean, and σ is the standard deviation of the distribution of x.

Plugging the given values, we have

z = (2.14 - 1.9) / 0.12 = 2.00

Using the 68-95-99.7 rule, the percentage of drivers having a reaction time of more than 2.14 seconds isP(z > 2) ≈ 0.05 (from the 99.7% section of the normal distribution curve)

Therefore, approximately 5% of drivers have a reaction time of more than 2.14 seconds.

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