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7.4 Use Normal Distributions

7.4 Use Normal Distributions. 7.3-7.4 HW Quiz: August 18 7.3-7.4 Quiz: August 20. Vocabulary. Normal Distribution Is modeled by a bell-shaped curve called a normal curve that is symmetric about the mean. The total area under the related curve is 1.

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7.4 Use Normal Distributions

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  1. 7.4Use Normal Distributions 7.3-7.4 HW Quiz: August 18 7.3-7.4 Quiz: August 20

  2. Vocabulary • Normal Distribution Is modeled by a bell-shaped curve called a normal curve that is symmetric about the mean. • The total area under the related curve is 1. • The percentage of the area covered by each standard deviation from the mean is shown in the graph. (on the next slide).

  3. Graph of a Normal Curve: σ = 1 standard deviation

  4. Vocabulary • Standard Normal Distribution Is the normal distribution with mean 0 and standard deviation 1.

  5. Example 1: • A normal distribution has mean x and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution. P(x > x + σ) P(x < x < x + σ)

  6. You Try: • A normal distribution has mean x and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution. P(x < x + σ) P(x < x < x + 2σ)

  7. Example 2: • The heights (in feet) of fully grown white oak trees are normally distributed with a mean of 90 feet and a standard deviation of 3.5 feet. • About what percent of white oak trees have heights between 86.5 feet and 93.5 feet?

  8. Formula • The formula below can be used to transform x-values from a normal distribution with mean x and standard deviation σ into z-values having a standard normal distribution.

  9. Z-Value • The z-value for a particular x-value is called the z-score for the x-value and is the number of standard deviation the x-value lies above or below the mean x. ***To use the z-score you will need to look at the table that is on p. 296 in your textbook***

  10. Example 3: • Use the information about white oak trees from Example 2 to answer the following. • Find the probability that a randomly selected white oak tree has a height of at most 94 feet. • You need to find the z-score (use the formula) • Now you need to use the Standard Normal Table

  11. You Try: • In the following exercises, refer to Example 2. • About what percent of white oak trees have height between 83 feet and 90 feet. • Find the probability that a randomly selected white oak tree has a height of at most 85 feet.

  12. Homework P. 266 #1-19odd

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