Final answer:
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.