Final answer:
To find the probability of a sample having an average greater than a given value, calculate the z-score using the provided formula and use a standard normal distribution table or statistical software to find the probability. Conduct a statistical test to confirm the results.
Step-by-step explanation:
To calculate the probability that the average amount of a sample of 34 cans is greater than 16.01 ounces, we need to use the z-score formula and the standard deviation of the sample mean. The formula is:
z = (x - μ) / (σ / √n),
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. For this question, x = 16.01, μ = 16.00, σ = 0.143, and n = 34. By plugging in these values, we can calculate the z-score. Once we have the z-score, we can find the probability using a standard normal distribution table or a statistical software.
Based on the calculated probability, we can determine whether the cans are filled with an amount greater than 16 ounces. If the probability is significantly greater than 0.05 (the significance level for a 95% confidence interval), then we can conclude that the cans are likely filled with more than 16 ounces. However, a statistical test should be conducted to confirm the results.