Answer:
The conditions for the approximation have been met
Step-by-step explanation:
Random samples on both cases and
p∧o proportion of bags packaged on the old machine that are damaged
p∧n sample proportion of bags packaged on the new machine that are damaged
p∧c = ( p∧o + p∧n ) / (nO + nN )
p∧o = 15 % p∧o = 0,15 nO = 150
p∧o * nO = 0,15 *150 p∧o * nO = 22,5
p∧n = 8 % p∧n = 0,08 nN = 200
p∧n*nN = 0,08 * 200 p∧n*nN = 16
Both p∧n*nN and p∧o * nO are bigger than 5
Therefore both samples are big enough for the approximation of the binomial distribution to normal distribution
