Math Problem Statement
the distribution of scores on a recent test closely followed a normal distribution with a mean of 22 points and a standard deviation of 4 points . the teacher wants to transform the test scores so that they have an approximately normal distribution with a mean of 80 and a standard deviation of 10 points . to do this she will use , new score=a+b(old score). Find the values of a and b that the teacher should use to transform the distribution of test scores
Solution
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Linear Transformation
Formulas
new score = a + b × (old score)
b = σ_new / σ_old
a + b × μ_old = μ_new
Theorems
Properties of Normal Distribution
Linear Transformation of Random Variables
Suitable Grade Level
Grades 10-12
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