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 above 450 grams?
A)0.0002
B)0.9996
C)0.9998
D)0.0004
E)0.9994

Question

Quizplus · Accepted Answer

We need to calculate the probability that the mean weight of a 50-box case of crackers is above 450 grams, given that the packaging machine puts in the boxes with a mean of 465 grams and a standard deviation of 30 grams.
 
To do this, we can use the Central Limit Theorem, which tells us that the distribution of sample means will be approximately normal with a mean of 465 grams and a standard deviation of 30/sqrt(50) grams.

Z = (450 - 465) / (30/sqrt(50)) = -5sqrt(50) / 3
 
From the standard normal distribution table, the area to the right of -5.09 is 0.9998. Therefore, the probability that the mean weight of a 50-box case of crackers is above 450 grams is 0.9998. 
 
Hence, the answer is C) 0.9998.

The Weight of Crackers in a Box Is Stated to Be