The mean clotting time of blood is 738 sec with a standard...

The mean clotting time of blood is 7.38 sec, with a standard deviation of 3.6 sec. What is the probability that an individual will have a clotting time less than 6 sec or greater than 8 sec? P(X<6 or X>8)=P(X<6 or X>8)= Express your answer as a decimal value. Round to four decimal places if applicable.

Transcript

00:01 Given that the mean clotting time is 7 .45 seconds with a standard deviation of 3 .6, we're interested in what the probability is that the time will be less than 7 seconds or greater than 8 seconds.

00:14 And so we could go ahead and split these up.

00:16 And then we're going to convert these to z scores.

00:19 So we're really interested in finding a z score that is less than.

00:23 And then we'll always start with z is equal to our x minus mu divided by sigma and this will standardize it.

00:37 So in our case, we'll go ahead and write it out.

00:40 We have our x is 7 minus 7 .45, all divided by 3 .6.

00:54 And this turns into a negative .12.

01:03 So, in other words, we are looking for how much area is represented in a table, a z -score table, that is to the left, or smaller than negative .125.

01:17 So in the table i'm looking at, this would be between .4552 and .448.

01:26 So let's go ahead and take both of those values and let's divide those up.

01:32 So we have 0 .452, 0 .4522 plus 0 .4483 and then divide those in two because that was the z score.

01:51 So basically what i did is i looked up a z score between negative 0 .2 and negative 0 .13.

02:02 0 .12 and negative 0 .13.

02:06 And then i took the average of those two.

02:09 And that ended up giving an area to the left of the curve that is 0 .45 -025.

02:22 So, in other words, 45 % of the area is less than 7 here.

02:31 Okay, now we just need to find out what the probability that it's greater than 8.

02:35 So same thing, we're going to convert this to a z score here.

02:39 So this z score is going to be positive and it's greater than 8 minus 7 .45, all divided by 3 .6.

03:03 Okay, and let's see what this gets us.

03:06 So this will be 8 minus 7 .45 .5 .5 divided by 3 .6.

03:14 This will be a z score that is greater than go ahead and put it in green.

03:30 0 .153.

03:31 So i think if we just look at the z score of 0 .15, that would probably be just fine there.

03:37 So let's look that up on the next page.

03:39 So a z score of 1 .5.

03:43 Oh, yeah, we could go 1 .53 here, no problem...

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