Here are the essential concepts you must grasp in order to answer the question correctly.
Normal Distribution
The normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean (mu) and standard deviation (sigma). 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.
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Z-Score
A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. Z-scores allow for the comparison of scores from different normal distributions and are essential for finding probabilities associated with specific values in a normal distribution.
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Probability Calculation
Probability calculation in the context of normal distributions often involves finding the area under the curve for a specified range of values. This is typically done using Z-scores and standard normal distribution tables or software. For the question at hand, calculating P(x > 182) requires determining the Z-score for x = 182 and then finding the corresponding probability that represents the area to the right of this Z-score.
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