A study of one thousand teens found that the number of hours they spend on social networking sites each week is normally distributed with a mean of 20 hours. The population standard deviation is 2 hours. What is the 95% confidence interval for the mean?

The 95% confidence interval for the mean is lower confidence limit = 19.88, and upper confidence limit = 20.12. Some notations for confidence interval are (19.88, 20.12) or [19.88, 20.12]. 

Step-by-step explanation:

The answer to this question is to find two values that define an interval in which we can consider there is, with a certain probability, the population's mean .  

We have here important information from the question:

Since we know that the random variable is normally distributed, the sample means are also normally distributed. Then, we can pose mathematically this problem as follows:

[1]

In this way, we have enough information to solve it:

.

.

.  

Well, substituting each value in [1], we have:

Then

The value for

Therefore

As a result, we can say that the 95% confidence interval for the mean is lower confidence limit = 19.88 and upper confidence limit = 20.12.

Note: some authors described these limits as (19.88, 20.12), while others as [19.88, 20.12].      

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