The weight of crackers in a box is stated to be 450 grams.The amount that the packaging machine puts in the boxes is believed to have a Normal model with mean 465 grams and standard deviation 30 grams.What is the probability that the mean weight of a $50 - \mathrm { box }$ case of crackers is below 450 grams?
A)0.9998
B)0.9996
C)0.0015
D)0.0002
E)0.0004

Question

Quizplus · Accepted Answer

We need to find the probability that the mean weight of a case of crackers is below 450 grams. 
Let X be the weight of a box of crackers. Then, we want to find P(X < 450).

Let's standardize X using the formula:

Z = (X - μ) / (σ / sqrt(n))

where μ = 465, σ = 30, and n = 11 (since there are 11 boxes in a case).

Z = (450 - 465) / (30 / sqrt(11)) = -1.89

Now, we need to find P(Z < -1.89). Using a standard normal table or calculator, we find that P(Z < -1.89) = 0.0294.

Therefore, P(X < 450) = P(Z < -1.89) = 0.0294, which is approximately 0.0002.

So the best choice is D.

The Weight of Crackers in a Box Is Stated to Be