Texting and Driving. In Exercises 21–26, refer to the accompanying table, which describes probabilities for groups of five drivers. The random variable x is the number of drivers in a group who say that they text while driving (based on data from an Arity survey of drivers).

Range Rule of Thumb for Significant Events
Use the range rule of thumb to determine whether 1 is a significantly low number of drivers who say that they text while driving.

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Step 1: Understand the Range Rule of Thumb. This rule states that values are considered significantly low if they are below the mean minus two standard deviations, and significantly high if they are above the mean plus two standard deviations.

Step 2: Calculate the mean (μ) of the random variable x using the formula μ = Σ[x * P(x)], where x is the number of drivers and P(x) is the probability associated with each x value.

Step 3: Calculate the standard deviation (σ) using the formula σ = √Σ[(x - μ)^2 * P(x)], where x is the number of drivers, μ is the mean, and P(x) is the probability associated with each x value.

Step 4: Determine the lower threshold for significantly low values using the formula μ - 2σ. Compare the value of 1 (the number of drivers who say they text while driving) to this threshold.

Step 5: Interpret the result. If 1 is below the calculated threshold, it is considered significantly low. Otherwise, it is not considered significantly low.

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주요 개념

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Random Variable

A random variable is a numerical outcome of a random phenomenon. In this context, the random variable x represents the number of drivers in a group of five who report texting while driving. Understanding random variables is crucial for analyzing probabilities and making inferences about populations based on sample data.

Probability Distribution

A probability distribution describes how probabilities are assigned to each possible value of a random variable. The table provided shows the probability distribution for the random variable x, indicating the likelihood of each number of drivers (from 0 to 5) texting while driving. This distribution is essential for calculating expected values and assessing the significance of specific outcomes.

Range Rule of Thumb

The Range Rule of Thumb is a guideline used to determine whether a particular value is significantly low or high in a given context. It suggests that values beyond two standard deviations from the mean can be considered significant. In this case, applying the rule helps assess whether having only one driver texting while driving is statistically significant compared to the overall distribution.