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vova2212 [387]
2 years ago
13

Last years freshman class at big state university totaled 5,305 students of those 1258 received a merit scholarship to help offs

et 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
Mathematics
1 answer:
Leokris [45]2 years ago
4 0

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

<h3>Normal Probability Distribution</h3>

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

Z = \frac{X - \mu}{\sigma}

  • 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:

\mu = 3456, \sigma = 478

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

Z = \frac{X - \mu}{\sigma}

Z = \frac{4250 - 3456}{478}

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 brainly.com/question/15181104

#SPJ1

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