SOLUTION: The weight of food packed in certain containers has a mean of 16 ounces and a standard deviation of 0.6 ounces. There are 36 containers placed in a box for shipping. Find the proba

Algebra ->  Probability-and-statistics -> SOLUTION: The weight of food packed in certain containers has a mean of 16 ounces and a standard deviation of 0.6 ounces. There are 36 containers placed in a box for shipping. Find the proba      Log On


   

Question 427216: The weight of food packed in certain containers has a mean of 16 ounces and a standard deviation of 0.6 ounces. There are 36 containers placed in a box for shipping. Find the probability that a randomly picked box will weight over 580 ounces.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let X = r.v. representing the weight of certain containers.
Then the distribution in question is Y = 36X. This is also a normal distribution with mean E(Y) = E(36X) = 36E(X) = 36*16 = 576, and variance Var(Y) = Var(36X) = 36%5E2Var%28X%29+=+1296Var%28X%29+=+1296%280.6%29%5E2 = 466.56. The standard deviation is thus sqrt%28466.56%29+=+21.6. You're looking for the probability P%28Y+%3E+580%29+=+P%28Z+=+%28Y+-+576%29%2F21.6+%3E+%28580+-+576%29%2F21.6+=+0.185%29, or P(Z > 0.185). Now use any table of standard normal probabilities.