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Unit 6 – Data Analysis and Probability

Unit 6 – Data Analysis and Probability. 6.2 – Use Normal Distributions. Georgia Performance Standards. MM3D2a – Determine intervals about the mean that include a given percent of data. MM3D2b – Determine the probability that a given value falls within a specified interval

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Unit 6 – Data Analysis and Probability

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  1. Unit 6 – Data Analysis and Probability 6.2 – Use Normal Distributions

  2. Georgia Performance Standards MM3D2a – Determine intervals about the mean that include a given percent of data. MM3D2b – Determine the probability that a given value falls within a specified interval MM3D2c – Estimate how many items in a population fall within a specified interval.

  3. Vocabulary A normal distribution is modeled by a bell-shaped curve called a normal curve that is symmetric about the mean. A normal distribution with mean x and standard deviation has the following properties. The total area under the related normal curve is 1. the percent of the area covered by each standard deviation is shown in the graph.

  4. Normal Distribution

  5. What is Standard Deviation? The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you you have a relatively large standard deviation.

  6. Vocabulary The standard normal distribution is the normal distribution with mean 0 and standard deviation 1. the formula below can be used to transform x-values from a normal distribution with mean x and standard deviation into z-values having a standard normal distribution.

  7. Z-scores The z-value for a particular x-value is called the z-score for the x-value and is the number of standard deviations the x-value lies above or below the mean x. To find the probability that z is less than or equal to some given value, use the standard normal table (next slide)

  8. Standard Normal Table

  9. Example 1: Find a normal probability A normal distribution has mean x and standard deviation . For a randomly selected x-value from the distribution, find P(x ≤ x ≤ x + 3).

  10. Finding Normal Probabilities A normal distribution has mean x and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

  11. Example 2: Interpret normally distributed data The heights of 3000 women at a particular college are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. About how many of these women have heights between 62.5 inches and 67.5 inches?

  12. Use a z-score and the standard normal table In Example 2 (women going to college), find the probability that a randomly selected college woman has a height of at most 68 inches.

  13. Guided Practice for Examples 2 and 3 • Guided Practice (Page 221) • 4-6

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