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Reviewing Normal Distributions and Z-scores

Reviewing Normal Distributions and Z-scores. from Math III. You will need : White board & marker Calculator Z-score Table FFM Sheet (eventually). REMINDER: .

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Reviewing Normal Distributions and Z-scores

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  1. Reviewing Normal Distributions and Z-scores from Math III • You will need: • White board & marker • Calculator • Z-score Table • FFM Sheet (eventually)

  2. REMINDER: • The Standard Normal Distribution is a normal distribution with a mean of 0 and a standard deviation of 1. To more easily compute the probability of a particular observation given a normally distributed variable, we can transform any normal distribution to this standard normal distribution using the following formula: • ; ; • When you find this value for a given value, it is referred to as the z-score. • The z-score is a standard score for a data value that indicates the number of standard deviations that the data value is away from its respective mean.

  3. 1.) Given a normal distribution with a a.) What data value corresponds to a z-score of 1.5?

  4. 1.) Given a normal distribution with a b.) What data value corresponds to a z-score of ?

  5. 2.) Given a normal distribution with a Calculate the z-score for: a.) X = 65

  6. 2.) Given a normal distribution with a Calculate the z-score for: b.) X = 90

  7. 2.) Given a normal distribution with a Calculate the z-score for: c.) X = 82.5

  8. 3.) Given a normal distribution with a Determine the X value which corresponds to the following z-scores: a.) Z = HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.

  9. 3.) Given a normal distribution with a Determine the X value which corresponds to the following z-scores: b.) Z = 0.75 HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.

  10. 3.) Given a normal distribution with a Determine the X value which corresponds to the following z-scores: c.) Z = 1.9 HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.

  11. 4.) Given a normal distribution with a Using the empirical rule, a.) what percent of the data falls between and ? b.) what x-values would correspond to (a) to contain that same percentage of data?

  12. 4.) Given a normal distribution with a Using the empirical rule, c.) what percent of the data falls between and ? d.) what x-values would correspond to (c) to contain that same percentage of data?

  13. 4.) Given a normal distribution with a Using the empirical rule, e.) What percent of the data falls to the LEFT of ?

  14. 4.) Given a normal distribution with a Using the empirical rule, f.) What percent of the data falls to the LEFT of ?

  15. 4.) Given a normal distribution with a Using the empirical rule, g.) What percent of the data falls to the RIGHT of ?

  16. FFM 8/16/13: In a normal distribution with and , 1.) find X if 2.) find P() = _____ 3.) P 48.2)

  17. A.M. III HOMEWORK Section 9.2, pg. 588-590 # 9.20 #9.22 #9.24 #9.28

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