The sample space of a population being researched contains 58 values and a mean of 318.6. the population has a known standard deviation of 29.2. identify the margin of error for a 95% confidence interval estimate of the mean of the population.

We have the following data:

Sample size = n = 58

Sample mean = x = 318.6

Population Standard Deviation = s = 29.2

Confidence Level = 95%

Since the population standard deviation is known, we can use z distribution to find the critical values for the 95% confidence interval. The z value from z table for 95% confidence interval comes out to be

z = 1.96

The confidence interval for the population mean will be:

Using the values of all the variables, we get:

Thus the 95% confidence interval about the population mean is (311.09 , 326.11).

Conclusion:

We are 95% confident that the true value of population means is between the bounds of the confidence interval i.e. between 311.09 and 326.11

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5