A sample of 120 bags of potatoes produced by a factory was found to have a mean weight of
2.47 kg and a standard deviation of 0.12 kg. Obtain a 95% confidence interval for the mean weight of all bags of potatoes produced by the factory.
see your standard Z table. Here is a useful site:
http://davidmlane.com/hyperstat/z_table.html
To obtain a 95% confidence interval for the mean weight of all bags of potatoes produced by the factory, we can use the formula:
Confidence Interval = Mean ± (Critical Value × Standard Error)
1. Calculate the critical value: Since we want a 95% confidence interval, we need to find the Z-score corresponding to a confidence level of 95%. This is known as the critical value. You can look up the critical value for a 95% confidence level in a Z-table or use a calculator. In this case, the critical value is approximately 1.96.
2. Calculate the standard error: The standard error measures the variability in the sample mean from sample to sample. It can be calculated using the formula:
Standard Error = Standard Deviation / sqrt(sample size)
In this case, the sample size is 120 bags of potatoes, and the standard deviation is 0.12 kg. Therefore:
Standard Error = 0.12 / sqrt(120) ≈ 0.01096 kg
3. Calculate the confidence interval: Now, we can substitute the values into the formula to calculate the confidence interval:
Confidence Interval = 2.47 ± (1.96 × 0.01096)
Calculating the lower bound:
Lower Bound = 2.47 - (1.96 × 0.01096) ≈ 2.4481 kg
Calculating the upper bound:
Upper Bound = 2.47 + (1.96 × 0.01096) ≈ 2.4919 kg
Therefore, the 95% confidence interval for the mean weight of all bags of potatoes produced by the factory is approximately 2.4481 kg to 2.4919 kg.