hagersaid380
Answered

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On a test that has a normal distribution, a score of 19 falls one standard deviation below the mean, and a score of 40 falls two standard deviations above the mean. Determine the mean of this test.

Sagot :

leena

Hi there!

We can use the following equation:

[tex]\large\boxed{z = \frac{x-\mu}{\sigma}}[/tex]

z = amount of standard deviations away a value is from the mean (z-score)

σ = standard deviation

x = value

μ = mean

Plug in the knowns for both and rearrange to solve for the mean:

[tex]-1 = \frac{19-\mu}{\sigma}\\\\-\sigma = 19 - \mu\\\\ \sigma = -19 + \mu[/tex]

Other given:

[tex]2 = \frac{40-\mu}{\sigma}\\\\2\sigma = 40- \mu\\\\ \sigma = 20 - \frac{\mu}{2}[/tex]

Set both equal to each other and solve:

[tex]-19 + \mu = 20 - \frac{\mu}{2}\\\\\frac{3\mu}{2} = 39 \\\\3\mu = 78 \\\\\boxed{\mu = 26 }[/tex]

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