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Last years freshman class at big state university totaled 5,305 students of those 1258 received a merit scholarship to help offset tuition costs their freshman year.the amount received was n(3456, 478) if the full cost was 4250 what percentage of students receive a merit scholarship did not receive enough to cover full tuition

Respuesta :

Using the normal distribution, it is found that 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.

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 mean and the standard deviation for the amounts are given as follows:

[tex]\mu = 3456, \sigma = 478[/tex]

The proportion is the p-value of Z when X = 4250, hence:

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

[tex]Z = \frac{4250 - 3456}{478}[/tex]

Z = 1.66

Z = 1.66 has a p-value of 0.9515.

Hence 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.

More can be learned about the normal distribution at https://brainly.com/question/15181104

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