Suppose the contents of bottles of water coming off a produc

Suppose the contents of bottles of water coming off a production line have a normal distribution with mean 16.3 ounces and standard deviation 0.2 ounce. If only 0.6% of the bottles exceed weight w, what is the value of w? Compute probabilities using the standard normal table in Appendix B (Table 3). Round the answer to one decimal place

Solution

Normal Distribution
Mean ( u ) =16.3
Standard Deviation ( sd )=0.2
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.06
Value of z to the cumulative probability of 0.06 from normal table is 1.55
P( x-u/ (s.d) > x - 16.3/0.2) = 0.06
That is, ( x - 16.3/0.2) = 1.55
--> x = 1.55 * 0.2+16.3 = 16.611 ~ 16.6