ONLY PROBLEM $4$ PLEASE

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QUESTION $4$

Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of $21$ gallons per week and a standard deviation of $3\mathrm{.}5$ gallons per week. Lead time is two days, and the dairy is open seven days a week.

Now an order is place when there is a supply of $8$ gallons on hand. One day after placing an order with the supplier, the manager receives a call from the supplier that the order will be delayed because of problems at the supplier's plant. The supplier promises to have the order there in two days.

After hanging up$,$ the manager checks the supply of walnut fudge ice cream and finds that $2$ gallons have been sold since the order was placed. Assuming the supplier's promise is valid, what is the probability that the dairy will run out of this flavor before the shipment arrives?

$0\mathrm{.}1423$

$0\mathrm{.}4168$

$0\mathrm{.}5832$

$0\mathrm{.}8577$