Practice/Exercises: Solve the following problems. 1. 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?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Please answer the exercise and sketch the normal curve
b. Step 1. Convert the score 38 to z-score
Z=
X-X
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. 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 Z= X-X 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. 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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