Fruit tart is one of the favorites at Hills Cafe. Every morning, the caf manager orders fresh tarts from Prairie Bakery to be sold at Hills during the day. Manager buys a tart at $5 and sells it at a price of $10. Daily fruit tart demand is normally distributed with a mean of 400 tarts and a standard deviation of100. Leftover tarts at the end of the day will be sold at a discounted price of $2/tart.

Note: The questions in sections (a) - (e) below are independent. That is, in each section use the information given above unless otherwise is stated in that specific section. For instance, in section (b) demand information is given as uniform distribution. In this section use uniform demand distribution. However, in the remaining sections, use the demand information of normal distribution as given in the original question above.

a): Given the information above, how many fruit tarts should the manager order each morning?

b): If the demand had a uniform distribution between 300 and 700, how many tarts should the manager order each morning?

c): Suppose a customer who is unable to purchase a fruit tart (due to stock out), settles for buying a muffin. A muffin sells for $6 and costs $4 each. Hills Cafe never runs out of muffins. In this case, how many fruit tarts would the manager order each morning?

d): Suppose it costs $1 to keep a tart in the store for a day. This holding cost is incurred only for the tarts that are not sold by the end of the day. In this case, how many fruit tarts would the manager order each morning?

e) (7 pts): If the manager orders 600 fruit tarts in the morning, what is the probability that Hills Cafe will sell all the tarts by the end of the day?