Question

The company who produces Rattlesnake Stout is having a bottling issue. Bottles of beverage claim to contain 16 ounces. Customers are reporting that some bottles “ are underfilled” The company’s bottling team sets the equipment so that bottles are filled so that the mean (μ) = 16.00 ounces (as labeled) and the standard deviation (σ) = 0.143 ounces. To check on consumer complaints, the team collects a random sample of 34 bottles and calculates the mean number of ounces (x) = 15.9 ounces

What is the probability that a single bottle of the beverage contains 15.9 ounces if the filling machines do not need adjusting?

Make a well labeled sketch of the sampling distribution for samples of 34 cans. Include the 68-95-99.7 rule cut offs.

What is the probability of getting a sample of 34 cans with an average of 15.9 ounces? Should the production team adjust their equipment to address customer concerns?

(Please show all of your work, thank you)

Answer 1

The z-score for X = 15.9 is

The probability that a single bottle of the beverage contains 15.9 ounces if the filling machines do not need adjusting is

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Sample size: n=34

The sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

Following is the graph:

The z-score for is

So,

Since probability is very small so the production team should not adjust their equipment to address customer concerns.