Question

The distribution of actual weights of 8 oz wedges of cheddar cheese produced at a dairy is normal with mean 8.1 ounces and standard deviation 0.1 ounces. If a sample of four of these cheese wedges is selected, what is the probability that their average weight is less than 8 oz?

Answer 1

To find the probability, calculate the standard error of the mean, standardize the value, and look it up in the standard normal distribution table.

Step-by-step explanation:

To find the probability that the average weight of a sample of four cheese wedges is less than 8 oz, we need to standardize the value and then look it up in the standard normal distribution table.

First, we calculate the standard error of the mean using the formula: s/sqrt(n), where s is the standard deviation of the population and n is the sample size.

Next, we standardize the value by subtracting the population mean from the desired average weight of 8 oz and dividing it by the standard error of the mean.

Finally, we look up the standardized value in the standard normal distribution table to find the corresponding probability.

In this case, the standard deviation of the weight of cheese wedges is 0.1 oz, the sample size is 4, and the desired average weight is 8 oz. Using the formula, we calculate the standard error of the mean as 0.1/sqrt(4) = 0.05 oz. The standardized value is (8 - 8.1)/0.05 = -2. To find the probability, we look up the value -2 in the standard normal distribution table, which is approximately 0.0228.