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Practice/Exercises: Solve the following problems. 1. Consider the normal distribution of IQs with a mean of 100 and a standard deviation of 16. What percent of IQs are a. greater than 95? b. less than 120? c. between 90 and 110? 2. A normal distribution of scores has a mean of 120 and a standard deviation of 20. What score separates the top 40% of the scores from the rest?

Practice/Exercises: Solve the following problems. 1. Consider the normal distribution of IQs with a mean of 100 and a standard deviation of 16. What percent of IQs are a. greater than 95? b. less than 120? c. between 90 and 110? 2. A normal distribution of scores has a mean of 120 and a standard deviation of 20. What score separates the top 40% of the scores from the rest?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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Note: Please follow the steps in the given lesson and sketch the normal curve
Practice/Exercises: Solve the following problems. 1. Consider the normal distribution of IQs with a mean of 100 and a standard deviation of 16. What percent of IQs are a. greater than 95? b. less than 120? c. between 90 and 110? 2. A normal distribution of scores has a mean of 120 and a standard deviation of 20. What score separates the top 40% of the scores from the rest?
Transcribed Image Text:Practice/Exercises: Solve the following problems. 1. Consider the normal distribution of IQs with a mean of 100 and a standard deviation of 16. What percent of IQs are a. greater than 95? b. less than 120? c. between 90 and 110? 2. A normal distribution of scores has a mean of 120 and a standard deviation of 20. What score separates the top 40% of the scores from the rest?
Example 3. Solution: In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie a. above score 50? b. below score 38? a. Step 1. Convert the score 50 to z-score X-X Z = = 50-45 4 z = 1.25 Step 2. Sketch the normal curve. 0 45 Let A area above z = 1.25 A₁ = area between z = 0 and z = 1.25 A₂ = area of half the curve From the table, A₁ = 0.3944 A = A₂-A₁ = 0.5-0.3944 A = 0.1056 The probability that a score picked up at random will be above score 50 is 0.1056. b. Step 1. Convert the score 38 to z-score Z= X-X S 38-45 = 2= -1.75 Step 2. Sketch the normal curve. -1.75 38 Let A = area below z = -1.75 A₁ = area between z = 0 and z = -1.75 A₂ = area of half the curve From the table, A₁ = 0.4599 A = A₂-A₁ = 0.5-0.4599 A = 0.0401 The probability that a score picked up at random will lie below 38 is 0.0401. ← A₂ A1 A1 A2 A 1.25 50 0 45
Transcribed Image Text:Example 3. Solution: In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie a. above score 50? b. below score 38? a. Step 1. Convert the score 50 to z-score X-X Z = = 50-45 4 z = 1.25 Step 2. Sketch the normal curve. 0 45 Let A area above z = 1.25 A₁ = area between z = 0 and z = 1.25 A₂ = area of half the curve From the table, A₁ = 0.3944 A = A₂-A₁ = 0.5-0.3944 A = 0.1056 The probability that a score picked up at random will be above score 50 is 0.1056. b. Step 1. Convert the score 38 to z-score Z= X-X S 38-45 = 2= -1.75 Step 2. Sketch the normal curve. -1.75 38 Let A = area below z = -1.75 A₁ = area between z = 0 and z = -1.75 A₂ = area of half the curve From the table, A₁ = 0.4599 A = A₂-A₁ = 0.5-0.4599 A = 0.0401 The probability that a score picked up at random will lie below 38 is 0.0401. ← A₂ A1 A1 A2 A 1.25 50 0 45
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