A confidence interval for a population mean has a margin of error of 3.1.

a)Determine the length of the confidence interval.
b)If the sample mean is 56.7, obtain the confidence interval.

a)


± 3.1

b)

56.7 - 3.1 = 53.6
56.7 + 3.1 = 59.8

Interval is 53.6 to 59.8

the population of 1500 construction truck has load distributed normally with the mean of 6 tons and the standard deviation of 1 ton. Find the probability that its load is greater than 7?

a) Well, if the margin of error is 3.1, then the length of the confidence interval is obviously... 6.2! Just double that margin of error and voila!

b) Alright, let's calculate that confidence interval for you now. If the sample mean is 56.7 and the margin of error is 3.1, we can subtract the margin of error from the sample mean to get the lower bound and add it to the sample mean to get the upper bound. So, the confidence interval is [53.6, 59.8]. That's where the true population mean is likely to fall. But hey, don't worry, I'm sure it won't fall too hard.

To determine the length of the confidence interval, we need to multiply the margin of error by 2. The margin of error is the maximum distance between the sample mean and the true population mean.

a) Length of the Confidence Interval = 2 * Margin of Error
Length of the Confidence Interval = 2 * 3.1
Length of the Confidence Interval = 6.2

Therefore, the length of the confidence interval is 6.2.

b) To obtain the confidence interval when the sample mean is 56.7, we need to add and subtract the margin of error from the sample mean.

Confidence Interval = Sample Mean ± Margin of Error
Confidence Interval = 56.7 ± 3.1

Lower Limit = 56.7 - 3.1 = 53.6
Upper Limit = 56.7 + 3.1 = 59.8

Therefore, the confidence interval for the population mean, when the sample mean is 56.7, is (53.6, 59.8).