The weights of packages received by a department store have

The weights of packages received by a department store have a mean of 300 lb and a standard deviation of 50 lb. What is the probability that 25 packages received at random and loaded on an elevator will exceed the safety limit of the elevator, listed as 8200 lb?

ANSWER: 0.0026

Solution

Mean ( u ) =300
Standard Deviation ( sd )=50
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
              
P(X > 328) = (328-300)/50/ Sqrt ( 25 )
= 28/10= 2.8
= P ( Z >2.8) From Standard Normal Table
= 0.0026