Respuesta :

Using the normal distribution, it is found that IQ scores above 124 would be considered unusually high.

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

  • The Z-score measures how many standard deviations the measure is from the mean.
  • If a measure is more than 2 standard deviations above the mean, that is, Z > 2, it is considered unusually high.

  • Distribution N(104,10) means that the mean is 104 and the standard deviation is 10, that is, [tex]\mu = 104, \sigma = 10[/tex]
  • For unusually high scores, we need Z > 2, thus, scores above X when Z = 2 are unusually high.

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

[tex]2 = \frac{X - 104}{10}[/tex]

[tex]X - 104 = 20[/tex]

[tex]X = 124[/tex]

Thus, IQ scores above 124 are considered unusually high.

A similar problem is given at https://brainly.com/question/14929706

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