lead time is the time between placing an order and having th

lead time is the time between placing an order and having the product avialable to satisfy customer deand. Intested in average lead time, u, for aparticular supplier of men\'s apparel, the purchasing department of a national department store chain radomly sampled 50 of the supplier\'s lead times and found x=47 days.

Solution

Normal Distribution
Mean ( u ) =42
Standard Deviation ( sd )=15
Number ( n ) = 50
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
a)
P(X < 47) = (47-42)/15/ Sqrt ( 50 )
= 5/2.1213= 2.357
= P ( Z <2.357) From Standard NOrmal Table
= 0.9908                  
P(X > = 47) = 1 - P(X < 47)
= 1 - 0.9908 = 0.0092