New studies by Federal Highway Administration traffic...

New studies by Federal Highway Administration traffic engineers suggest that speed limits on many thorough-fares are set arbitrarily and often are artificially low. According to traffic engineers, the ideal limit should be the “85th percentile speed.” This means the speed at or below which 85 percent of the traffic moves. Assuming speeds are normally distributed, find the 85th percentile speed for roads with the following conditions. Source: Federal Highway Administration. The mean speed is 52 mph with a standard deviation of 8 mph.

New studies by Federal Highway Administration traffic engineers suggest that speed limits on many thorough-fares are set arbitrarily and often are artificially low. According to traffic engineers, the ideal limit should be the “85th percentile speed.” This means the speed at or below which 85 percent of the traffic moves. Assuming speeds are normally distributed, find the 85th percentile speed for roads with the following conditions. Source: Federal Highway Administration.

The mean speed is 52 mph with a standard deviation of 8 mph.

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Key Concepts

Inverse Cumulative Distribution Function

Also known as the quantile function, this function is used to determine the value or z-score corresponding to a specified cumulative probability (or percentile) in a distribution. It is essential for finding thresholds, such as the 85th percentile, in a normally distributed dataset.

Normal Distribution

A common continuous probability distribution characterized by its symmetric, bell-shaped curve. It is defined by two parameters—the mean and the standard deviation—which determine the center and the spread of the distribution, respectively.

Percentiles

Percentiles are values below which a certain percentage of data falls in a distribution. They are used to understand the relative standing of a value within the entire set of observations.

Z-Score Transformation

The z-score transformation converts a data point from a normal distribution to a standard normal distribution by subtracting the mean and dividing by the standard deviation. This standardization allows for the use of universal tables or functions to find probabilities and percentiles.

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