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Section 2

Section 2. Standard Units and Areas under the Standard Normal Distribution. z = x -. Standard score (z score). z score. The z value or z score tells us the number of standard deviations the original measurement is from the mean.

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Section 2

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  1. Section 2 Standard Units and Areas under the Standard Normal Distribution

  2. z = x - Standard score (z score)

  3. z score • The z value or z score tells us the number of standard deviations the original measurement is from the mean. • The mean of the original distribution is always zero in standard units. • An x value in the original distribution that is above the mean has a positive z value. • An x value in the original distribution that is below the mean has a negative z value.

  4. Example • The scores on an aptitude test are approximately normally distributed with mean = 500 points and standard deviation = 100 points. Find the proportion of males who received the following scores. A. between 500 and 600 B. between 400 and 600

  5. Example The length of a pregnancy is a normal random variable with a mean of 266 days and standard deviation of 16 days. Find the proportion of pregnancies that are between 285 days and 305 days.

  6. More examples using the Table • To the right of z = 0 • To the left of z = 1.43 • To the left of z = -1.34 • To the right of z = 2.35 • To the right of z = -0.87 • The area between 1.23 and 2.78

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