The probability model below describes the number of repair...

The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. $$\begin{array}{l|c|c|c|c}\text { Repair Calls } & 0 & 1 & 2 & 3 \\\hline \text { Probability } & 0.1 & 0.3 & 0.4 & 0.2\end{array}$$ a) How many calls should the shop expect per hour? b) What is the standard deviation?

The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.
$$\begin{array}{l|c|c|c|c}\text { Repair Calls } & 0 & 1 & 2 & 3 \\\hline \text { Probability } & 0.1 & 0.3 & 0.4 & 0.2\end{array}$$
a) How many calls should the shop expect per hour?
b) What is the standard deviation?

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Key Concepts

Discrete Probability Distribution

A discrete probability distribution assigns probabilities to a countable set of outcomes. In the context of repair calls per hour, each possible number of calls (e.g., 0, 1, 2, 3) is an outcome in the distribution, and its probability indicates how likely that outcome is to occur during any given hour.

Expected Value

The expected value is the weighted average of all possible outcomes of a random variable. It is calculated by multiplying each outcome by its probability and then summing these products. In probability and statistics, the expected value serves as a measure of the central tendency, giving a prediction of the average outcome over many trials.

Variance and Standard Deviation

The variance measures the spread of a set of data points or the distribution of a random variable around its mean, calculated as the average of the squared deviations from the expected value. The standard deviation is the square root of the variance, providing a measure of dispersion that is in the same units as the original variable. These concepts are crucial in quantifying the uncertainty or risk associated with a random variable's outcomes.

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