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(c) The teacher wants to transform the test scores so that they have an approximately Normal

distribution with a mean of 80 points and a standard deviation of 10 points. To do this, she will

use a formula in the form:

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.

Respuesta :

frika

Answer:

[tex]a=-8\\ \\b=0.1[/tex]

Step-by-step explanation:

Use formula

[tex]Z=\dfrac{X-\mu}{\sigma},[/tex]

where

[tex]Z[/tex] = new score

[tex]X[/tex] = old score

[tex]\mu[/tex] = the mean

[tex]\sigma[/tex] = standard deviation

In your case,

[tex]\mu=80\\ \\\sigma=10[/tex]

Hence,

[tex]Z=\dfrac{X-80}{10}\\ \\Z=\dfrac{X}{10}-\dfrac{80}{10}\\ \\Z=0.1X-8\\ \\Z=-8+0.1X[/tex]

So,

[tex]a=-8\\ \\b=0.1[/tex]

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