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5.1 Introduction to Normal Distributions and the Standard Normal Distribution

5.1 Introduction to Normal Distributions and the Standard Normal Distribution. Important Concepts: Normal Distribution Standard Normal Distribution Finding Areas Below the Standard Normal Curve. 5.1 Introduction to Normal Distributions and the Standard Normal Distribution.

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5.1 Introduction to Normal Distributions and the Standard Normal Distribution

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  1. 5.1 Introduction to Normal Distributions and the Standard Normal Distribution • Important Concepts: • Normal Distribution • Standard Normal Distribution • Finding Areas Below the Standard Normal Curve

  2. 5.1 Introduction to Normal Distributions and the Standard Normal Distribution • What is a normal distribution? • A continuous probability distribution for a random variable X. • The graph of a normal distribution is called the normal curve. • The shape of a normal curve is determined by two parameters – the mean and the standard deviation of the random variable (see p. 235).

  3. 5.1 Introduction to Normal Distributions and the Standard Normal Distribution • If a variable is normally distributed, or follows a normal distribution, what does that tell us? • The mean, median, and mode of the variable are all equal. • The normal curve is bell-shaped and is symmetric about the mean. • The total area below the normal curve is 1. • The tails of the normal curve are asymptotic to the x-axis. • Inflection points are located one standard deviation away from the mean.

  4. 5.1 Introduction to Normal Distributions and the Standard Normal Distribution • Examples of continuous random variables that are normally distributed, i.e., follow a normal distribution: • The heights and weights of adult males and females • The body temperatures of rats • The cholesterol levels of adults • Intelligence Quotients (IQ Scores) • Life spans of light bulbs • Weights of newborn infants

  5. 5.1 Introduction to Normal Distributions and the Standard Normal Distribution • The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. • Very important relationship we will need later: • If X is a normally distributed variable with mean µ and standard deviation σ, then the variable follows the standard normal distribution.

  6. 5.1 Introduction to Normal Distributions and the Standard Normal Distribution • Finding areas below the standard normal curve. • We use Table 4 to find cumulative areas #18 p. 243 (area to the left) #26* (area to the left) #20 (area to the right) #32 (area between two values) • Standard normal curves and probabilities #48 p. 245 #54 #56

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