Let x= red blood cell (RBC) count in millions per cubic...

Let $x=$ red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, $x$ has an approximately normal distribution with mean $\mu=4.8$ and standard deviation $\sigma=0.3$ (based on information from Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse Press). Convert each of the following $x$ intervals to $z$ intervals. (g) Interpretation If a female had an $\mathrm{RBC}$ count of 5.9 or higher, would that be considered unusually high? Explain using $z$ values and Figure $7-12$.

Let $x=$ red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, $x$ has an approximately normal distribution with mean $\mu=4.8$ and standard deviation $\sigma=0.3$ (based on information from Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse Press). Convert each of the following $x$ intervals to $z$ intervals.
(g) Interpretation If a female had an $\mathrm{RBC}$ count of 5.9 or higher, would that be considered unusually high? Explain using $z$ values and Figure $7-12$.

Transcript

00:01 So we're given a distribution for red blood cell count, and we're saying that the average red blood cell count is 4 .8, and that a standard deviation is 0 .3.

00:13 So let's just go out a little bit, and here's 5 .1, here's 5 .4, here's 5 .7.

00:21 And if we subtract away, 0 .3, we're at 4 .5, we're at 4 .2, we're at 3 .9.

00:30 And we want to convert these into z values.

00:34 So what's the likelihood? 4 .5 is less than x.

00:38 And so if we take our, we know our z score is equal to our score minus the mean divided by the standard deviation.

00:47 So converting this, we would take that 4 .5 minus the mean divided by a standard deviation.

00:54 And we can actually see that right there on the score right here, that 4 .5 was corresponding to a negative 1.

01:03 Part b asked us, what about 4 .2 if i have x greater than, excuse me, less than 4 .2.

01:14 Well, we can see that that corresponds to a value of the z score being less than negative 2.

01:21 Part c, if we want to find the probability of being between 4 and 5 .5, and we use this conversion.

01:33 So basically i'm going to substitute my 4 in here.

01:37 And so we have the 4 minus the 4 .8 divided by the 0 .3.

01:45 And that's going to come out to approximately negative 2 .67.

01:51 Now that's a z value.

01:53 And then likewise substitute this in here.

01:58 And so change that to a 5 .5.

02:03 And i'll have to do a little insert 5 .5.

02:07 And that gives me me a value of positive 2 .33.

02:12 And again, if i look at where 5 .5 would be about right here, that makes sense if that's going to be a score of 2 .33.

02:20 And likewise, a 4 is going to be right here, and that value of negative 2 .67 looks correct.

02:27 So let's keep going.

02:29 Now we want to convert these into a score.

02:32 We know the z score is a negative 1 .44...

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