Based on the analysis of 50 randomly selected weekdays, with an average count of 83 cars and a standard deviation of 10 cars, we can be 99.5% confident that the mean number of cars passing the intersection between 11am and 12pm each weekday is between approximately 79.043 and 86.957.
To determine the confidence interval for the mean number of cars passing the intersection between 11am and 12pm each weekday, we can use the standard deviation and the sample mean. Given that we have randomly selected 50 weekdays and the average count is 83 cars with a standard deviation of 10 cars, we can calculate the confidence interval with 99.5% confidence.
1. Find the critical value:
- Since we want a 99.5% confidence level, we need to find the critical value corresponding to that confidence level.
- The critical value can be obtained from the z-table or a statistical calculator.
- For a 99.5% confidence level, the critical value is approximately 2.807.
2. Calculate the margin of error:
- The margin of error is determined by multiplying the critical value by the standard deviation divided by the square root of the sample size.
- In this case, the standard deviation is 10 cars and the sample size is 50 weekdays.
- Therefore, the margin of error is (2.807 * 10) / √50 ≈ 3.957.
3. Determine the confidence interval:
- The confidence interval is calculated by subtracting and adding the margin of error to the sample mean.
- Given that the sample mean is 83 cars, the lower bound of the confidence interval is 83 - 3.957 ≈ 79.043, and the upper bound is 83 + 3.957 ≈ 86.957.
4. Interpret the confidence interval:
- We can be 99.5% confident that the mean number of cars passing the intersection between 11am and 12pm each weekday is between approximately 79.043 and 86.957.