Question

Last year’s freshman class at Big State University totaled 5,340 students. Of those, 1,252 received a merit scholarship to help offset tuition costs their freshman year (although the amount varied per student). The amount a student received was N($3,462, $482). If the cost of full tuition was $4,150 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition? (Round your answer to the nearest whole percent.)

Percentage of students %

Answer 1

The scholarship amount is normally distributed with mean = $3,462 and standard deviation = $482

Tuition fee = $4,150

For normally distributed data, P(X < A) = P(Z < (A - mean)/standard deviation)

Here, a student did not receive enough to cover full tuition is his/her scholarship amount is less than $4,150

Probability that the scholarship amount is less than $4,150, P(X < 4150)

= P(Z < (4150 - 3462)/482)

= P(Z < 1.43)

= 0.9236 (take the probability value corresponding to 1.43 from standard normal distribution table)

= 92%

Percentage of students who received a merit scholarship did not receive enough to cover full tuition = 92%