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The scores on a mathematics college-entry exam are normally distributed with a mean of 68 and standard deviation 7.2. Students scoring higher than one standard deviation above the mean will not be enrolled in the mathematics tutoring program. How many of the 750 incoming students can be expected to be enrolled in the tutoring program?

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Arlene138

631 is the answer-I’m taking this castle learning rn

Using the normal distribution, it is found that 631 of the 750 incoming students can be expected to be enrolled in the tutoring program.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The proportion of students who score one standard deviation below the mean is the p-value of Z = 1, hence it is of 0.8413.

Hence, out of 750 students, the number is given by:

0.8413 x 750 = 631 students can be expected to be enrolled in the tutoring program.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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