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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?

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?

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
Section: Chapter Questions
Problem 22SGR
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b. Step 1. Convert the score 38 to z-score X-X Z= S = 38-45 4 Z = -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. 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? A2 A1 0 45
Transcribed Image Text:b. Step 1. Convert the score 38 to z-score X-X Z= S = 38-45 4 Z = -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. 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? A2 A1 0 45
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