Question

Commencement Every year at commencement, the president hands out diploma covers to joyous students that cross the front of the auditorium to accept the cover and a hearty handshake. Commencement exercises have averaged 850 students with a standard deviation of 70 the last several years. The bookstore can provide a box of 144 diploma covers for $2,000 but is unwilling to break bulk. Any additional diploma covers must be purchased on the black market at $15 each.

How many gross of diploma covers should be ordered from the bookstore?
A) 3
B) 4
C) 5
D) 6

Answer 1

To determine the number of gross of diploma covers that should be ordered from the bookstore, we need to calculate the total number of covers needed and then divide by the number of covers in a gross. The average number of students at commencement is 850, and the standard deviation is 70. Assuming a Z-score of 2 (which corresponds to a probability of 97.7%), the covers needed would be 990. Therefore, we should order 7 gross of diploma covers from the bookstore.

Step-by-step explanation:

To determine the number of gross of diploma covers that should be ordered from the bookstore, we need to calculate the total number of covers needed and then divide by the number of covers in a gross.

The average number of students at commencement is 850, and the standard deviation is 70. We want to ensure that we have enough covers for all students, so we need to account for the possibility of having more students than the average.

To calculate the number of covers needed, we can use the formula:

Covers needed = Average number of students + (Z-Score * Standard deviation)

Assuming a Z-score of 2 (which corresponds to a probability of 97.7%), the covers needed would be:

Covers needed = 850 + (2 * 70) = 990

Now, to calculate the number of gross of covers needed, we divide the total covers needed by the number of covers in a gross:

Gross of covers needed = Covers needed / 144

Gross of covers needed = 990 / 144 = 6.875

Since we cannot order a fraction of a gross, we round up to the nearest whole number, which is 7. Therefore, we should order 7 gross of diploma covers from the bookstore.