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The normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean (μ) and standard deviation (σ). It is symmetric around the mean, meaning that approximately 68% of the data falls within one standard deviation from the mean, and about 95% falls within two standard deviations. This distribution is fundamental in statistics as many real-world phenomena tend to follow this pattern.

A Z-score represents the number of standard deviations a data point is from the mean of a distribution. It is calculated using the formula Z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation. Z-scores are essential for standardizing different normal distributions, allowing for the comparison of probabilities across different datasets.

Calculating probabilities for a normal distribution involves finding the area under the curve between two points, which can be done using Z-scores and standard normal distribution tables or software. For the given range P(19.6 < x < 26.1), one would first convert the values to Z-scores, then use the cumulative distribution function (CDF) to find the probabilities associated with these Z-scores and subtract them to find the desired probability.