The lifetime of a smartphone battery while playing video is described by a normal model. if 95% of batteries last between 8.5 and 11.5 hours, what are the mean and standard deviation of the distribution of battery lifetime while playing videos?

We need to find the mean of these two numbers which is 8.5 and 11.5.To find the mean we just simply add and then divide by the total number in the set.
(8.5 + 11.5) / 2 = 10
Second, we need to subtract the mean from the first number in the data set, and we need to square the differences.
8.5 - 10 = -1.5^2 = 2.2511.5 - 10 = 1.5^2 = 2.25 
Next, we will add the squared differences and we will then divide the total by the number of items.
2.25 + 2.25 = 4.50 / 2 = 2.25
We will next calculate the square root of this mean of the differences to find the standard deviation. 
sqrt(2.25) = 1.5

10 is the mean while 1.5 is the standard deviation of the distribution of battery lifetime while playing videos.