Question

1. At the start of the month, there are 750 units of a given product in stock. Sales per month follow a normal distribution where μ = 700 and σ = 25 (what we in fact have is a discrete distribution; the normal distribution should therefore be viewed as an approximation).
a. Calculate the probability that the stock will be used up by the end of the month
b. The supplier wants to reduce the risk of running out of stock to 0.5%.
What level of stock should he maintain at the start of the month?
c. halfway through the month, there are still 400 units in stock. What is now the
probability of running out of stock at the end of the month?

Answer 1

a)

µ =    700          
σ =    25          
              
P( X ≤    750   ) = P( (X-µ)/σ ≤ (750-700) /25)      
=P(Z ≤   2.00   ) =   0.97725   (answer)

b)

µ=   700  
σ =    25  
P(X≤x) = 1-0.005 = 0.99500  
      
z value at 0.995=   2.5758   (excel formula =NORMSINV(0.995))
z=(x-µ)/σ      
so, X=zσ+µ=   2.576   *25+700
X =   764.396   (answer)

c)

µ =    350          
σ =    12.5          
              
P( X ≤    400   ) = P( (X-µ)/σ ≤ (400-350) /12.5)      
=P(Z ≤   4.00   ) =   0.99997   (answer)