Anvils Works' requires, on average, $2,900$ tons of aluminum each week, with a standard deviation of $800$ tons. The lead time to receive its orders is $8$ weeks. The holding cost for one ton of aluminum for one week is $$10.$ It operates with a $0\mathrm{.}98$ in$-$stock probability.

a$.$ On average, how many tons does it have on order?

Note: Round your answer to nearest integer.

Tons

b$.$ On average, how many tons does it have on hand?

Note: Do not round intermediate calculations. Round your answer to nearest integer.

Tons

c$.$ If its average inventory was $8,500$ tons, what would be its average holding cost per week?

Note: Round your answer to nearest integer.

Average holding cost per week

d$.$ If its average inventory was $7,000$ tons, what would be its average holding cost per ton of aluminum?

Note: Round your answer to $2$ decimal places.

Average holding cost per ton

e$.$ Suppose its on$-$hand inventory is $5,200$ tons, on average. What in$-$stock probability does it offer to its customers? Hint: use the $=$NORM.S$.$DIST$($z$,1)$ Excel function.

Note: Do not round intermediate calculations or your z value. Round your final answer to $4$ decimal places.

In$-$stock probability