00:01
In this problem we're told that the lifetime of a dvd player is normally distributed with a mean of 8 years and a standard deviation of 46 months.
00:14
That says we take a sample of 42 dvd players, so our sample size n is 42, and we're asked to find the probability of its average lifespan being less than 84 months.
00:24
So we're finding the probability of x bar being less than 84.
00:28
Let me fix that less than sign.
00:34
Less than 84.
00:35
Okay.
00:36
So before we can do anything, we have to make sure that our mean and standard deviation are in the same units, because right now one is in years and one is in months.
00:44
So let's just convert everything to months.
00:46
So to do that for the mean, we just multiply 8 by 12.
00:51
When we multiply 8 by 12, we get 96.
00:55
So our mean here is 96.
00:58
Next we need to realize that we're dealing with a sample.
01:00
Since that sample size n is greater than 30, that means that we need to find our mean for the sampling distribution, as well as our standard deviation for the sampling distribution.
01:10
Our mean for the sampling distribution is always equal to our population mean, which is 96...