The amount of corn chips dispensed into a 16-ounce bag by the dispensing machine has been identified at

possessing a normal distribution with a mean of 16.5 ounces and a standard deviation of 0.1 ounce. Suppose 400
bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean
weight of these 400 bags exceeded 16.6 ounces

Actually, I believe it's approximately zero.

Source: I have a MS in Mathematics

Pardon me... approximately zero if the standard deviation is 0.2 ozs.

Z = (mean1 - mean2)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

To find the probability that the sample mean weight of these 400 bags exceeded 16.6 ounces, we can use the central limit theorem and the properties of the normal distribution.

1. The central limit theorem states that for a large enough sample size (n > 30), the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution.
2. The mean of the sample means will be equal to the population mean (16.5 ounces).
3. The standard deviation of the sample means (also known as the standard error) can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the standard error is 0.1 ounces divided by the square root of 400 (which equals 0.1/20 = 0.005).

Now, to find the probability that the sample mean weight of these 400 bags exceeded 16.6 ounces, we need to find the area under the normal distribution curve to the right of 16.6 ounces.

1. Standardize the value (16.6) by subtracting the population mean (16.5) and dividing by the standard error (0.005). This gives us a standardized value of (16.6 - 16.5) / 0.005 = 20.
2. Look up the probability associated with the standardized value of 20 in the standard normal distribution table or use a calculator or statistical software.
3. The probability that the sample mean weight of these 400 bags exceeded 16.6 ounces is equal to 1 minus the probability associated with the standardized value of 20.

Remember, the normal distribution table provides the probability for values up to a given standardized value. To find the probability to the right of a standardized value, you subtract the table value from 1.

Using a standard normal distribution table or a calculator, we find that the probability associated with a standardized value of 20 is extremely close to 1. As a result, the probability that the sample mean weight of these 400 bags exceeded 16.6 ounces is essentially 0 (or very close to 0).

Therefore, the probability is almost 0 that the sample mean weight of these 400 bags exceeded 16.6 ounces.

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0.3085