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-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

The mean weight of a 50-box case of crackers is the sample mean weight of 50 boxes, which follows a Normal distribution with mean 465 grams and standard deviation of 30 grams divided by the square root of 50 (the standard error of the mean). 
Thus, the z-score for a mean weight of 450 grams is:
z = (450 - 465) / (30 / sqrt(50)) = -5sqrt(50)/3
Using a standard Normal table or calculator, we can find the probability that a standard Normal random variable is less than -5sqrt(50)/3, which is approximately 0.0002. Therefore, the probability that the mean weight of a 50-box case of crackers is below 450 grams is 0.0002. 
Hence, the best answer is D.

The Weight of Crackers in a Box Is Stated to Be