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Answer :
Final answer:
The probability that the mean of a sample of 36 16-ounce bottles of water is less than 15.9 ounces is approximately 0.82%.
Explanation:
To find the probability that the mean of a random sample of thirty-six 16-ounce bottles of water is less than 15.9 ounces, we can use the central limit theorem. First, we calculate the standard error of the mean using the formula: standard deviation / square root of sample size. In this case, the standard deviation is 0.5 ounces and the sample size is 36 ounces. Therefore, the standard error of the mean is 0.5 / √36 = 0.0833 ounces. Next, we standardize the sample mean by subtracting the desired mean (15.9 ounces) from the population mean (16.1 ounces) and dividing by the standard error of the mean. So the standardized value is (15.9 - 16.1) / 0.0833 = -2.4. Finally, we calculate the probability using a standard normal distribution table or calculator. The probability that the mean of this sample is less than 15.9 ounces is approximately 0.0082, or 0.82%.
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