Problem#18.  General Normal Distribution

Use Excel to compute the following for a normal distributed random variable Z with m=400 and s =65.

a) P(Z > 500)=?

b) P( 335 ≤ Z ≤  465)=?

c) Find the value of C such that P(X > C) = 0.1.

Problem #19.  General Normal Distribution

An electronics retailer has only 100 webcams left in stock until the next shipment arrives from a supplier in 5 days.  The demand for the webcams is known to be normal distributed. The mean demand for webcams in the next 5 days is expected to be 80 and the standard deviation is 14.

Use Excel to compute the following.

a) What is the probability that the retailer will sell out the webcam inventory within the next 5 days?

b) What is the probability that the retailer will have 10 or more units remaining in stock when the next shipment arrives? 

c) If the retailer had ordered the webcams earlier (i.e. before the stock level dropped to 100 units), then the risk of a stockout would have been lower. What is the correct “reorder point” (the stock level at the time the retailer contacts the supplier for a new shipment) if the retailer wants the probability of a stock out until the next shipment arrives to be at or below 1%?