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The machinery at a food packing plant is able to put exactly 12 ounces of juice

ID: 3332500 • Letter: T

Question

The machinery at a food packing plant is able to put exactly 12 ounces of juice in every bottle. However, some items such as apples common variable sizes so it is almost impossible to get exactly 3 pounds of apples in a bag labeled "3 pounds". Therefore, the machinery is said to put an average of = 50 ounces (3 pounds 2 ounces) in each bag. The distribution of bag weights is approximately normal with a standard deviation of = 6 ounces.

a) What is the probability of randomly picking 9 bags of apples that weighs less than 46 ounces? Make sure to show your work.

Explanation / Answer

Mean = 50 ounces

Sigma = 6 ounces

We use the normal distribution params to solve the problem, we normalize the distribution:

a. P(X<46)

= P(Z< (46-50) / (6/sqrt(9))

= P(Z<-2)

= .0228

So, probability of randomly picking 9 bags of apples that weighs less than 46 ounces 2.28%