Normal Distribution — Normal distribution

About this lesson

This unit introduces the normal distribution, a continuous probability distribution characterized by a bell-shaped, symmetric curve defined by the mean (μ) and standard deviation (σ). It covers properties of the normal curve, including symmetry, total area under the curve equaling 1, and the empirical rule that approximately 68.26%, 95.44%, and 99.74% of data lie within 1, 2, and 3 standard deviations from the mean, respectively. The unit then explains the standard normal distribution (Z), which has mean 0 and standard deviation 1, and shows how to convert any normal random variable X to Z using the formula Z = (X - μ)/σ. Students learn to use a standard normal table to find probabilities for intervals, including those involving negative Z values, using symmetry. Worked examples and exercises involve finding probabilities for given Z values, solving for unknown Z values (k) given probabilities, and converting between X and Z to solve problems about real-world data like student heights and weights. By the end, students should be able to calculate probabilities for normal and standard normal variables, find Z or X values corresponding to given probabilities, and apply these skills to practical scenarios.