Question

An automatic coffee vending machine dispenses a different amount of coffee in millilitres (mL) for each cup. Assume that the following nine measurements were taken from a population with a normal distribution: 185, 170, 196, 176, 173, 187, 193, 170 and 173 mL. Construct an 80% confidence interval for the mean amount of coffee that is dispensed for all cups of coffee from this machine.

Answer 1

To construct an 80% confidence interval for the mean amount of coffee dispensed by the vending machine, calculate the sample mean and sample standard deviation. Using the formula for calculating the margin of error and the Z-score for an 80% confidence level, the confidence interval can be calculated as (sample mean - margin of error, sample mean + margin of error). The 80% confidence interval for the mean amount of coffee dispensed is (174.07, 183.49) mL.

Step-by-step explanation:

To construct a confidence interval for the mean amount of coffee dispensed by the vending machine, we first need to calculate the sample mean and the sample standard deviation. For the given data set, the sample mean is 178.78 mL and the sample standard deviation is 9.06 mL.

Next, we can calculate the margin of error using the formula:

Margin of Error = (Z-score) x (Standard deviation / sqrt(n)),

where n is the sample size, which is 9 in this case.

For a confidence level of 80%, the Z-score is 1.28. Plugging in the values, the margin of error is (1.28) x (9.06 / sqrt(9)) = 4.71 mL.

The confidence interval can be calculated as (sample mean - margin of error, sample mean + margin of error). So, the 80% confidence interval for the mean amount of coffee dispensed is (178.78 - 4.71, 178.78 + 4.71), which simplifies to (174.07, 183.49) mL.