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Name: 2.2 Notetaking Guide AP Statistics Standardized Scores What is a z-score? Why do we Standardize? EXAMPLE: The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 points. Suppose that weights of all such animal can be described by a NORMAL model with a standard deviation of 84 pounds. How many standard deviations from the mean would a steer weighing 1000 pounds be? The z-chart! Where are the blue sheets? Using the table to find percentages from z-scores Find P(z < -1.46) Find P(z > -1.46) The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 points. Suppose that weights of all such animal can be described by a Normal model with a standard deviation of 84 pounds. What proportion of the steers would weigh less than 1000 pounds? Which would be more unusual, a steer weighing 1000 pounds or a steer weighing 1250 pounds? Using the table to find z-scores from percentages In a standard normal model, what value(s) of z cut(s) off the region described? DRAW A PICTURE. The highest 20% The highest 75% The lowest 3% The middle 90% EXAMPLE Scores on the SAT verbal test in recent years follow approximately the normal distribution, with mean of 505 and sd 110. How high must a student score in order to place in the top 10% of all students taking the SAT? FINDING PROPORTION OF SCORES ABOVE, BELOW, OR BETWEEN Z-SCORES NORMAL PROBABILITY PLOT GIVEN THE PROPORTION OF SCORES BELOW A VALUE, FIND Z-SCORE.