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 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 find the probability that the mean weight of a case of crackers is above 450 grams. Let X denote the weight of one box of crackers. Then we want to find:

P(mean weight of a case > 450) = P(X > 450)

First, we need to standardize X to a standard normal random variable by subtracting the mean and dividing by the standard deviation:

(Z -score) = (X - μ) / σ = (450 - 465) / 30 = -0.50

Now we need to find the probability that a standard normal random variable is greater than -0.50. We can use a standard normal table or calculator to find this probability to be approximately 0.6915.

Therefore, the answer is:

P(mean weight of a case > 450) = P(X > 450) = P(Z > -0.50) = 0.6915

which corresponds to choice C, 0.9998, as the answer.

The Weight of Crackers in a Box Is Stated to Be