A manufacturing company measures the weight of boxes before

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and a standard deviation of 90 lbs., and 24 lbs., respectively, then based on the sample size of 36 boxes, the probability that the average weight of the boxes will exceed 94 lbs is :

a) 34.13%

b) 84.13%

c) 15.87%

d) 56.36%

Solution

Mean ( u ) =90
Standard Deviation ( sd )=24
Number ( n ) = 36
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 94) = (94-90)/24/ Sqrt ( 36 )
= 4/4= 1
= P ( Z >1) From Standard Normal Table
= 0.1587

ANS: c) 15.87%