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Section 2 Standard Units and Areas under the Standard Normal Distribution
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Standard score (z score) z = x -
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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.
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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
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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.
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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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