Question

Two bottling plants package a certain type of sports drink. Suppose the mean volume of all of this type of sports drinks is 20 fluid ounces. Bottling plant A bottles an average of 50,000 sports drinks per day. Bottling plant B bottles an average of 175,000 sports drinks per day. On a particular day, which bottling plant is less likely to record a mean volume of 21 fluid ounces for the day?

The two bottling plants are equally likely to record such a volume because random samples from both plants will have daily mean volumes that vary.

Bottling plant A (with 50,000 sports drinks per day), because with fewer sports drinks there will be less variability in the daily mean volume.

Bottling plant B (with 175,000 sports drinks per day), because the daily mean will be closer to 20 fluid ounces with more sports drinks in the sample.

Answer 1

Bottling plant B (with 175,000 sports drinks per day), because the daily mean will be closer to 20 fluid ounces with more sports drinks in the sample.

When we produce more and more sports drink, the population mean would come closer and closer to 20 fluid ounces as the sample reaches population, there would be less variability in the mean drink amount. So On a particular day, PLANT B bottling plant is less likely to record a mean volume of 21 fluid ounces for the day

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