The length of time that it takes Ken to drive to work...

The length of time that it takes Ken to drive to work represents a normal distribution with a
mean of 25 minutes and a standard deviation of 4.5 minutes. If Ken allows 35 minutes to get
to work, what percent of the time can he expect to be late?

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Key Concepts

Normal Distribution

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is characterized by its bell-shaped curve and is commonly used in statistics to model real-valued random variables whose distributions are not known.

Mean

The mean is a measure of central tendency that represents the average of all values in a distribution. In the context of a normal distribution, it is the center point of the distribution, around which the data values are symmetrically distributed.

Standard Deviation

The standard deviation is a measure of the spread or dispersion of a set of values in a distribution. In a normal distribution, it determines the width of the curve; a larger standard deviation indicates that the data points are spread out over a wider range of values.

Z-Score (Standard Score)

The z-score is a statistical measurement that describes a value's relation to the mean of a group of values. It is calculated by subtracting the mean from the value and dividing by the standard deviation. This transformation allows one to use standard normal distribution tables to determine probabilities associated with specific values.

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