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

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Presentation transcript:

Section 2 Standard Units and Areas under the Standard Normal Distribution

Standard score (z score) z = x -

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.

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

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.

More examples using the Table To the right of z = 0 To the left of z = 1.43 To the left of z = To the right of z = 2.35 To the right of z = The area between 1.23 and 2.78