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Suppose that you are conducting a survey on how many students have blue eyes in each first period classroom at Garfield Middle school. The mean number of blue-eyed students is 6, and the standard deviation is 2. Mr. Garcia's first period history class has 10 students with blue eyes. What statement is true?

The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean,

The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the left of the mean,

The number of blue-eyed students in Mr. Garcia's class is 4 standard deviations to the right of the mean,

The number of blue-eyed students in Mr. Garcia's class is 4 standard deviations to the left of the mean

Respuesta :

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Answer:

  • The correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean

Explanation:

To calculate how many standard deviations a particular value in a group is from the mean, you can use the z-score:

      [tex]z-score=(x-\mu )/\sigma[/tex]

Where:

  • [tex]z-score[/tex] is the number of standard deviations the value of x is from the mean
  • [tex]\mu[/tex]  is the mean
  • [tex]\sigma[/tex]  is the standard deviation

Substitute in the formula:

       [tex]z-score=(10-6)/2=4/2=2[/tex]

Which means that the number of blue-eyed students in Mr. Garcia's class is 2 standard deviations above the mean.

Above the mean is the same that to the right of the mean, because the in the normal standard probability graph the central value is Z = 0 (the z-score of the mean value is 0), the positive values are to the right of the central value, and the negative values are to the left of the central value.

Therefore, the correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean,

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