Normal distribution

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The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric around its mean. It is commonly used in statistics to describe real-valued random variables that tend to cluster around a central value.

Concepts

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean represents the center of the distribution, while the standard deviation determines the spread or variability of the data.

AP Style Example Questions

What is the probability of a randomly selected individual having a height within one standard deviation of the mean?

How do you calculate the z-score for a given data point in a normal distribution?

What is the relationship between the mean, median, and mode in a normal distribution?

Answers to the Example Questions

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

The z-score can be calculated by subtracting the mean from the data point and dividing the result by the standard deviation.

In a normal distribution, the mean, median, and mode are all equal.

AP Style Exercises

Calculate the z-score for a data point of 75 in a normal distribution with a mean of 60 and a standard deviation of 10.

Determine the area under the curve between z = -1 and z = 1 in a standard normal distribution.

Find the data point that corresponds to a z-score of -2 in a normal distribution with a mean of 50 and a standard deviation of 5.

Answers to the Exercises

The z-score for a data point of 75 is (75 - 60) / 10 = 1.5.

The area under the curve between z = -1 and z = 1 in a standard normal distribution is approximately 68%.

The data point that corresponds to a z-score of -2 is -2 * 5 + 50 = 40.

Remember to practice these concepts and exercises to strengthen your understanding of the normal distribution. Happy learning!