On a list: When a production process is operating correctly, the number of units produced per hour has a normal distribution.

a. Find the mean of the sampling distribution of the sample means:
\[ E(\bar{X}) = 100 \]
(Type an integer or a decimal.)

b. Find the variance of the sample mean:
\[ \sigma^2 = 16 \]
(Type an integer or a decimal.)

c. Find the standard error of the sample mean:
\[ \sigma_{\bar{X}} = 4 \]
(Type an integer or a decimal.)

d. What is the probability that the sample mean exceeds 100.8?
\[ P(\bar{X} > 100.8) = \]
(Round to four decimal places as needed.)

The mean of the sampling distribution of the sample means is 100. The variance of the sample mean is 16. The standard error of the sample mean is 4. The probability that the sample mean exceeds 100.8 can be calculated.

a. The mean of the sampling distribution of the sample means, denoted as E(x), is given as 100. This means that, on average, the sample means will cluster around 100.

b. The variance of the sample mean, denoted as σ^2(X), is given as 16. Variance measures the spread of the distribution. A larger variance indicates more dispersion of sample means around the mean.

c. The standard error of the sample mean, denoted as σ(X), is the square root of the variance, which in this case is 4. It measures the average amount of error between the sample mean and the population mean.

d. To find the probability that the sample mean exceeds 100.8, we can use the standard error. We subtract the population mean (100) from 100.8 and divide by the standard error (4) to obtain the z-score. Then, we can look up the corresponding probability from the standard normal distribution table or use a calculator.

Learn more about probability : brainly.com/question/31828911

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