Weekly demand for packs of a certain make of chocolate trifle at a major supermarket store has a Normal distribution with mean of 200 and standard deviation of 40 packs.
(a) The Supermarket chain monitors weekly sales by categorising them according to whether they fall in the top 25%, middle 50% or the lowest 25% according to this distribution. What are the numbers of packs that define these 3 ranges?
My solution :use formula X-U/standard deviation under z>0.675 , -0.675<Z<0.675, z<-0.675, then ,X is the range


(b) What would be the probability that the store sells out of trifles by the end of a week if it restocks its fridge with chocolate trifles up to a stock level of 280 packs at the start of each week? Any unsold trifles need to be thrown away at the end of the week. Estimate the weekly wastage.
probability sell out 280: x-u/standard deviation, Z= 280-200/40= 2
p(z=2)=0.4772
P(X>280)=0.5-0.4772=0.0227



(c) In an attempt to reduce wastage the store manager decides to restock the fridge at the start of the week with sufficient packs to meet the demand in 90% of weeks.
(i) How many packs should he put in the fridge at the start of each week?
My solution: P=0.4,z=1.28
z=1.28=x-200/40,
X=251.2

(ii) What is the probability that the store runs out of trifles in at least two weeks in a period of one month (i.e. 4 weeks)?
(iii) What proportion of customers wanting to buy trifles will find the fridge empty under this policy? [This is intended to be challenging for the last few marks, and you may use Excel to perform calculations]


Can someone tell me how to solve the Estimate the weekly wastages and (C),(ii)(iii)

Many thanks in advance