A merit scholarship

Last year’s freshman class at Big State University totaled 5,307 students. Of those, 1,264 received a merit scholarship to help offset tuition costs during their freshman year (although the amount varied per student). The amount a student received was N($3,454, $490). If the cost of full tuition was $4,300 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?

Correct answer:

p =  95.79 %

Step-by-step explanation:

$$\begin{gathered} n=5307 \\ a=1264 \\ m=3454\text{USD} \\ \sigma =490\text{USD} \\ t\dots N(m,\sigma ) \\ p=N(t<4300) \\ \Delta m=4300-m=4300-3454=846\text{USD} \\ \Delta m\doteq 2\sigma \\ p=100\cdot 0.9579=95.79\% \end{gathered}$$

Use the normal distribution table.

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