The vice president of human resources. at Lowes is studying...

The vice president of human resources. at Lowes is studying the number of on-the-job accidents over a period of one month. He developed the following probability distribution. Compute the mean, variance, and standard deviation of the number of accidents in a month. $$\begin{array}{|cc|}\hline \text { Number of } & \\\text { Accidents } & \text { Probability } \\\hline 0 & .40 \\1 & .20 \\2 & .20 \\3 & .10 \\4 & .10 \\\hline\end{array}$$

The vice president of human resources. at Lowes is studying the number of on-the-job accidents over a period of one month. He developed the following probability distribution. Compute the mean, variance, and standard deviation of the number of accidents in a month.
$$\begin{array}{|cc|}\hline \text { Number of } & \\\text { Accidents } & \text { Probability } \\\hline 0 & .40 \\1 & .20 \\2 & .20 \\3 & .10 \\4 & .10 \\\hline\end{array}$$

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Key Concepts

Standard Deviation

The standard deviation is the square root of the variance. It provides a measure of spread in the same units as the original random variable, making it more interpretable. It indicates, on average, how much the outcomes deviate from the mean.

Discrete Probability Distribution

A discrete probability distribution assigns a probability to each possible discrete outcome of a random variable. It is used to describe the likelihood of various outcomes, where the probabilities of all outcomes sum to one. In contexts involving counts or events (such as accidents), this distribution helps in understanding and modeling real-world scenarios.

Expected Value (Mean)

The expected value, or mean, of a probability distribution is a weighted average of all possible outcomes, where each outcome is weighted by its probability. It provides a measure of the central tendency of the distribution, quantifying the long-run average outcome if an experiment is repeated many times.

Variance

Variance measures the dispersion of the random variable around the mean. It is calculated as the expected value of the squared deviations of each outcome from the mean, thereby quantifying how spread out the outcomes are. A higher variance indicates that the outcomes are more spread out from the mean.

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