Question

Fill in percents given by the Empirical Rule: What svmbols do we use for the following? What type of numerical variable is the following? possible values for the random variable. Number of green M&Ms in a bag of 30M&Ms:DC Number of inches of rainfall during the winter: DC When finding probabilities with a continuous numerical variable, we use a of values (rather than individual values), and probability is found by looking at the under a probability density curve (the probability for a single value is ). B. Empirical Rule Practice: Recall that the Empirical Rule gives us a rough idea of how much data is within 1,2 , or 3 standard deviations of

Answer 1

The Empirical Rule helps in understanding the probability distribution of a normal variable, stating roughly 68%, 95%, and 99.7% of data fall within one, two, and three standard deviations of the mean, respectively. Probabilities for discrete variables are found by counting, while for continuous variables, they are derived from areas under the probability density curve.

Step-by-step explanation:

The Empirical Rule is a statistical rule stating that for a normal distribution, about 68 percent of the data falls within one standard deviation of the mean, approximately 95 percent falls within two standard deviations, and about 99.7 percent falls within three standard deviations. This rule is particularly useful for understanding the behavior of random variables in a bell-shaped distribution.

Methods for calculating probabilities differ depending on whether the random variable is discrete or continuous. For discrete random variables, probabilities are calculated for countable outcomes. For continuous random variables, probabilities are found by looking at the area under a probability density curve; this is because the probability for a single precise value in a continuous distribution is actually zero.

When working with sample data and empirically estimating probabilities, as the sample size increases, the empirical probability tends to converge to the theoretical probability, a principle known as the law of large numbers. The Empirical Rule can be applied to sample data to help assess the probability of certain outcomes assuming the sample is representative of a normal distribution.