Answer:
The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml
Step-by-step explanation:
Standard deviation ( σ )= 0.250 ml
assume the required amount of chemical to be deposited in each syrup bottle to be X
Hence the distribution of X in each bottle can be represented as :
X Г N ( u , 0.250 )
for a bottle not to be rejected : P ( X ≤ 2 )
To determine the setting so that no more than 1% of the bottles of cough syrup prepared by this machine will be rejected we have to standardize the variable X
at X = 2 ml
z = = z ----------- ( 1 )
probability for a bottle to be rejected : P( x >2 ) = 1 - P ( x ≤ 2 )
= 0.01
attached below is a normal distribution curve showing probability values
from the curve
p( 0 < Z < z ) = 0.5 - 0.01 = 0.49
Area = 0.49 hence from the Normal table where area = 0.49 the value of z = 2.33
Referring back to equation 1 above: z = = 2.33 --------- (2)
<em>u</em> = mean value that should be added so that the bottle will not be rejected
make <em>u</em> subject of the equation : u = 2 - ( 2.33 * 0.250 )
u = 1.41750
The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml
