Suppose that 158 out of a random sample of 200 letters mailed in the United States were delivered the day after they were mailed. Based on this, compute a 90% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed. Then find the lower limit and upper limit of the 90% confidence interval.

The 90% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed is (0.7426, 0.8374). The lower limit is 0.7426 while the upper limit is of 0.8374.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

Suppose that 158 out of a random sample of 200 letters mailed in the United States were delivered the day after they were mailed.

This means that

90% confidence level

So , z is the value of Z that has a p-value of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 90% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed is (0.7426, 0.8374). The lower limit is 0.7426 while the upper limit is of 0.8374.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.