The manufacturer of a laser printer reports the mean number...

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,250. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 770 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. How many pages should the manufacturer advertise for each cartridge if it wants to be correct 95 percent of the time?

Transcript

00:01 All right, in your question, you're given information about laser printers.

00:03 You're told that the laser printer has a mean number of pages printed of 12 ,250, a standard deviation of 770, and it closely, the number of pages printed follows a normal model.

00:20 So the question is, imagine we're going to provide the advertising for this.

00:26 And we want to determine a page number that we could put on our advertising so that maybe we say you're going to be able to print at least this many pages and then we're going to be right 95 % of the time.

00:43 So what i would do here, just imagine what's occurring, i'm going to put a boundary line over here because i'm thinking this is going to be some number of pages.

00:55 And i'm just going to make this up.

00:56 This is not the actual answer yet, but let's just say it's 10 ,000 pages.

01:01 So imagine how we would write that.

01:05 We expect that this print cartridge will provide at least 10 ,000 pages of printing.

01:13 And we want to be correct 95 % of the time.

01:16 So we want the number of, you know, with outcomes higher than 10 ,000 pages.

01:21 We want to be up here.

01:23 We're only going to be wrong down here 5 % of the time when we're below that cover.

01:28 Off.

01:30 So the questions like this, it takes a minute to actually wrap your mind around which side of the boundary you're looking for.

01:38 So we want the 95 % to represent pages more than our cutoff.

01:44 So let me get rid of the 10 ,000 and let's figure out how we can do this.