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A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ is reported as a z-score, what would the z-score be?
a. z = m + 3
b. z = m + 3s
c. z = 3
d. cannot be determined from the information given

Respuesta :

Answer:

Option C) z = 3                                  

Step-by-step explanation:

We are given the following in the question:

IQ scores are normally distributed.

An IQ score is three standard deviations above the mean. Let x be the IQ score. Then, we can write,

[tex]x = \mu + 3\sigma[/tex]

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{\mu + 3\sigma-\mu}{\sigma} = \dfrac{3\sigma}{\sigma} = 3[/tex]

Thus, the z-score is 3.

Thus, the correct answer is

Option C) z = 3

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