The volume of honey in a bottle is not constant but it can b

The volume of honey in a bottle is not constant, but it can be modelled using a normal distribution with a mean of 16.5 oz.If the producer of the product is required by the FDA to fill 90% of the containers with 16( or more) oz od honey , what is the largest allowable value S the standard deviation, sigma? .57 .39 .24 .81

Solution

Normal Distribution
Mean ( u ) =16.5
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z < X ) = 0.9
Value of z to the cumulative probability of 0.9 from normal table is -1.282
P( X-u/s.d < X - 16.5/ s.d ) = 0.9
That is, ( 16 - 16.5/ s.d ) = -1.2816
--> s.d = ( 16 - 16.5 ) / -1.2816
--> s.d = ( -0.5 ) / -1.2816
--> s.d = 0.3902 ~ 0.39