Question

Problem 6. In a chemical process, three bottles of a standard fluid are emptied into a larger container. A study of the individual bottles shows that the mean value of the contents is 15 ounces (a) Find the expected value and the standard deviation of the volume of liquid emptied (b) If the content of the individual bottles is normally distributed, what is the probability and the standard deviation is 0.18 ounces. If three bottles form an i.i.d. sample, into the larger container. that the volume of liquid emptied into the larger container will be in excess of 45.6 ounces?

Answer 1

a)here value in larger container Y=x1+x2+x3

expected value (mean) in larger container E(Y)=E(X1)+E(X2)+E(X3) =15+15+15=45

and std deviation in large container SD(Y)=sqrt(Var(x1)+Var(x2)+Var(x3))=sqrt(0.18²+0.18²+0.18²)

=0.3118

b)

P(Y>45.6)=1-P(Y<45.6)=1-P(Z<(45.6-45)/0.3118)=1-P(Z<1.92)=1-0.9726 =0.0274