Question

Last year’s freshman class at Big State University totaled 5,303 students. Of those, 1,266 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($3,458, $473). If the cost of full tuition was $4,200 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 amount a student received was N($3,458, $473)

Mean = $3458

standard deviation = $473

the cost of full tuition was $4,200

Let, X be the amount received

P[ students who received a merit scholarship did not receive enough to cover full tuition ] = P[ X < 4200 ]

P[ X < 4200 ] = P[ ( X - mean(X))/sd(X) < ( 4200   - mean(X))/sd(X) ]

P[ X < 4200 ] = P[ ( X -3458)/21.75 < ( 4200   - 3458)/473 ]

P[ X < 4200 ] = P[ Z < 1.57 ]

P[ X < 4200 ] = 0.9418

P[ X < 4200 ] = 94.18%