Finding probabilities associated with distributions that are standard normal distributions is equivalent to probabilities associated with distributions that are standard normal distributions is equivalent to finding the area of the shaded region representing that probability. finding the variance of the distribution. finding the z-scores associated with the probabilities. f

The standard normal distribution, also known as the Z-distribution, is crucial in statistics because it allows us to calculate probabilities and percentiles using well-tabulated values. By standardizing a normal distribution (converting values to z-scores), we can observe and utilize the properties of symmetry and central tendency, making it easier to find areas under the curve that represent probabilities. When working with probabilities, a common mistake is ignoring the importance of z-scores. It's vital to correctly convert your raw scores to z-scores using the formula \( z = \frac{(X - \mu)}{\sigma} \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation. Forgetting this step might lead to miscalculating the area under the curve, resulting in incorrect probability assessments.