Final answer:
To construct a confidence interval for the mean delivery time, you need to know the sample mean, population standard deviation, and sample size. The formula is the sample mean plus or minus the product of the z-value and the standard deviation divided by the square root of the sample size. An example would be 36 minutes ± 1.397 minutes for a 90% confidence interval.
Step-by-step explanation:
When constructing a confidence interval for the population mean, we are estimating the range in which the true population mean is likely to fall. The confidence level (e.g., 95%, 90%, or 98%) indicates how sure we can be that the interval includes the true mean. Given that the population standard deviation (σ) is known, we can use the z-distribution to find the critical value for our confidence level and calculate the confidence interval using the formula:
Confidence Interval = Sample mean ± (Critical value * (Standard deviation / √Sample size))
Example for a 90% Confidence Interval:
If the mean delivery time is 36 minutes with a population standard deviation of 6 minutes and the sample size is 50, we'll first determine the critical z-value for a 90% confidence level, which is approximately 1.645. Then we calculate the margin of error by dividing the standard deviation (6) by the square root of the sample size (50) and multiplying by the critical value.
Margin of Error = 1.645 * (6 / √50)
The confidence interval is then:
36 ± (1.645 * (6 / √50)), which simplifies to 36 ± 1.397
Thus, we are approximately 90% confident that the true mean pizza-delivery time is between 34.603 and 37.397 minutes.