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**

**----------------**

**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.**

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