Homework graphing calculator Pencil red pen highlighter 1

Homework, graphing calculator, Pencil, red pen, highlighter 1. Draw and label a normal distribution curve, to 3 standard deviations, of an: a) IQ test with a mean of 100 and a standard deviation of 15. b) IQ test with a mean of 100 and a standard deviation of 10. 2. Ren scored a 130 on the first test, and Stimpy scored 130 on the second test. A score of 130 would be how many standard deviations from the mean on each graph? Hint:

a) 55 130 +7 labeled graph 70 85 b) +7 labeled graph 100 115 130 145 2) Ren’s IQ is 2 standard deviations from the mean. +1 Stimpy’s IQ is 3 standard deviations. +1 70 90 80 100 110 120 130 Notice one curve is wider and shorter than the other Notice that the same score is a different number of standard deviations away from the mean. Normal curve animation

Example #1: A college entrance exam has a mean score of 520 and a standard deviation of 100. Bobby scored a 670 on the exam. Label , , , and 220 320 420 520 620 720 820 Duhhh, I can 670 help. How many standard deviations is Bobby’s score from the mean? Shut up you Any guesses? idiot! Let the More than teach! one… less than 2. . . teacher

220 420 320 620 520 820 720 It is often useful to know how many standard deviations a data z–score point is above or below the mean. This is called the ____. Z= Mean of the data. _____ standard _____ deviation of the data. _____ 670 – 520 = 150 1. 5 = ____ Determine Bobby’s z–score. Z = 100 1. 5 standard deviation _______ above the Therefore, Bobby scored _____ mean.

220 320 420 520 620 720 – 3 – 2 – 1 0 1 2 Label the z–scores on your graph. 670 1. 5 Z–score is the number of standard deviations above or below the mean 820 3

Example #2: Using the information from the previous problem, determine the z–score for each person’s exam. Patty: 720 Jessica: 520 720– 520 100 = 200 100 520– 520 100 = 0. 75 = – 2. 2 =2 =0 Patty: 2 300– 520 100 = – 220 100 Judy: 0. 75 595– 520 100 = 75 100 Jim: -2. 2 = – 0. 5 Jim: 300 Jessica: 0 470– 520 100 = – 50 100 Judy: 595 Fred: -0. 5 Fred: 470 220 320 420 520 620 720 – 3 – 2 – 1 0 1 2 820 3

320 – 2 420 – 1 520 0 620 1 Patty: 2 Judy: 0. 75 Jessica: 0 Fred: -0. 5 Jim: -2. 2 220 – 3 720 2 Jim Who is the farthest from the mean? ______ positive Scores above the mean have _____ z–scores. negative z–scores. Scores below the mean have _____ 0 A score equal to the mean has a z–score of ______. 820 3

Example #3: The times (in seconds) for a PE class to run the ¼ mile are listed below. Record the times into L 1. First, determine = ______ 75 and = ______, 11. 72 then label , , , and below. 39. 84 – 3 51. 56 – 2 63. 28 – 1 75 0 86. 72 1 98. 44 2 110. 16 3 TIMES: 58, 102, 65, 70, 68, 75, 81, 84, 79, 68

Student # Time Z – score L 2 (seconds) 1 58 – 1. 45 Find the z–score for each time using LIST ALGEBRA. 2 102 2. 30 Use: 1–variable statistics: 3 65 – 0. 85 4 70 – 0. 43 5 68 – 0. 597 6 75 0 7 81 0. 51 8 84 0. 77 9 79 0. 34 10 68 – 0. 597 STAT CALC 1–VAR STATS LIST MATH MEAN ( … vars 5: statistics STO L 2 4: σx

Student # Time Z – score L 2 (seconds) 1 58 – 1. 45 2 102 2. 30 3 65 – 0. 85 4 70 – 0. 43 5 68 – 0. 597 6 75 0 7 81 0. 51 8 84 0. 77 9 79 0. 34 10 68 – 0. 597 Which student is the farthest from the mean? #2 Student # ___ 2 is _____ 2. 3 standard above the mean. deviations ______ However, in this case, above the not desirable. mean is _____ Outliers - Generally, if a point is 2 standard deviations more than ___ above or below the mean, it is outlier considered an _____. Is this student an outlier? Yes, the student is more than 2 standard deviations from the mean.

Practice: 1. Mrs. Windham gave a test in her Algebra 2 class. The scores were normally distributed with a mean of 80 and a , , and standard deviation of 7. Label , 59 – 3 66 – 2 a) If Melissa has a raw score of 92, what is her z– score? 92– 80 7 = 12 ≈ 1. 71 7 73 – 1 80 0 b) If Aiden has a raw score of 71, what is his z–score? 71– 80 7 = -9 ≈ – 1. 29 7 87 1 94 2 . 101 3 c) If Malique has a raw score of 60, what is his z–score? 60– 80 7 = -20 ≈ – 2. 86 7

59 – 3 66 – 2 73 – 1 80 0 87 1 94 2 101 3 d) Lee’s z–score was 1. 43. e) Amanda’s z–score was – 0. 72. Find his raw score on the test. Find her raw score on the test. 1. 43 = x – 780 – 0. 72 = x – 80 7 x – 80 = 7(– 0. 72) x – 80 = 7(1. 43) x – 80 = – 5. 04 x – 80 = 10. 01 x = 74. 96 x = 90. 01 x ≈ 90 x ≈ 75 f) Which students are outliers in the above problem? Malique is an outlier since he is 2σ from the mean.

2. The mean for each normal curve is given below, but the standard deviation is not given. Based on the graphs, how do the standard deviations compare between both graphs? Graph A Graph B The standard deviation is greater in Graph B than in Graph A. A larger standard deviation “stretches” the graph. We can also say that the data in Graph B is more spread out than in Graph A.

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