If records show that the amount of fill per bottle is normally distributed, with a standard deviation of .2 ounce, and if the bottling machine is set to produce a mean fil per bottle of 12.1 ounces, what is the approximate probability that the sample mean of the 10 test bottles is less than 12.2 ounces?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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To avoid difficulties with the Federal Trade Commission or state and local consumer
protection agencies, a beverage bottler must make reasonably certain that 12-ounce
bottles actually contain 12 ounces of beverage. To determine whether a bottling
machine is working satisfactorily, one bottler randomly samples 10 bottles per hour
and measures the amount of beverage in each bottle. The mean of the 10 fill
measurements is used to decide whether to readjust the amount of beverage
delivered per bottle by the filling machine.
If records show that the amount of fill per bottle is normally distributed, with a
standard deviation of .2 ounce, and if the bottling machine is set to produce a mean fill
per bottle of 12.1 ounces, what is the approximate probability that the sample mean
of the 10 test bottles is less than 12.2 ounces?
Transcribed Image Text:To avoid difficulties with the Federal Trade Commission or state and local consumer protection agencies, a beverage bottler must make reasonably certain that 12-ounce bottles actually contain 12 ounces of beverage. To determine whether a bottling machine is working satisfactorily, one bottler randomly samples 10 bottles per hour and measures the amount of beverage in each bottle. The mean of the 10 fill measurements is used to decide whether to readjust the amount of beverage delivered per bottle by the filling machine. If records show that the amount of fill per bottle is normally distributed, with a standard deviation of .2 ounce, and if the bottling machine is set to produce a mean fill per bottle of 12.1 ounces, what is the approximate probability that the sample mean of the 10 test bottles is less than 12.2 ounces?
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