Throwback question in pharmacologic research a variety of...

Throwback question: In pharmacologic research a variety of clinical chemistry measurements are routinely monitored closely for evidence of side effects of the medication under study. Suppose typical blood-glucose levels are normally distributed with mean 92.47 mg/dl and standard deviation 29.99 mg/dl. (Note: Round all of your answers to four decimal places where appropriate.) We would expect the blood glucose levels to fall between and in 99.7% of patients._______ A normal glucose range is 65 - 120 mg/dl. What is the probability a patient's blood glucose level falls between these two values? z1 = _____ z2 = _____ probability = _______ What is the probability that a patient's blood glucose level is greater than 52 mg/dl? z = ______ probability = ______ If a blood glucose level is in the top 2%, then the patient is classified as abnormal. What blood glucose level corresponds to this cut-off? z = ________ glucose =______ mg/dl

Transcript

00:01 There is given a normal distribution in this question and the mean, which is denoted by mu, that was given as 92 .47.

00:11 And what about the standard deviation? this is denoted by sigma.

00:17 This is given as 29 .99.

00:20 So i can just define the random variable x here.

00:22 This is normally distributed.

00:24 92 .47 and 29 .99 .99.

00:28 Great.

00:28 Rate.

00:29 So when we look at the first question, the glucose level fall between some values and the probability was 99 .7 % percent.

00:38 So for the first one, i can just use the empirical rule here, the empirical rule.

00:46 So that this rule says if you have a normal distribution, you can just graph this normal distribution, something like this one.

00:54 There is the mean value.

00:56 And if you just go away one standard deviation, this is 34%.

01:00 If you just go away to the left, this is again, 34%.

01:04 If you go away to standard division from the mean score, this is 13 .5%.

01:10 And this is also 13 .5 % here.

01:14 This is mu minus 2 standard division.

01:16 And this is mu plus 3 standard division, which is 2 .35%.

01:22 And this one is also mu minus 3 standard division, which is 2 .35%.

01:30 Great.

01:30 So when we just add all these probabilities here, so we will have, so the sum of all these probabilities, which is equal to 99 .7%.

01:41 So what about the values here? so the mean value here, 42 .97.

01:47 So i'm going to add one standard deviation to the right and subtract one standard division to the left.

01:53 So the first one, this is 92 .47.

01:57 I'm going to add one standard division, which is equal.

02:02 To 122 .46 and add 29 .99.

02:08 This is 152 .45 and add one more.

02:13 So add 29 .99.

02:15 So that would be 182 .44.

02:19 And what about if i subtract them? we will have, this is 92 .47 minus 29 .99.

02:26 That would be 62 .48 and minus 29 .99.

02:27 That would be 62 .48 and minus 29 .9.

02:32 This is 32 .49 and subtract 29 .99 that would be 2 .5 great so for the 99 for the 99 .7 percent it is is between mu minus three standard division and mu plus three standard division and we got these values as which is 2 .5 this is 2 .5 and 182 .44.

03:06 So this is the interval that we have for the first part of this question.

03:11 And what about the second question we have here? and what about the probability of between? so the probabilities of the x value, which is between 65 and 120.

03:27 So first of all, we need to just convert these values into the z values.

03:31 Let's say this is z1.

03:34 Let's say 465 we have the z1 value and for 120 we have the z2 value here so the z is equal to x minus move over standard division this is a formula so for z1 the x value here 65 minus the mean value so the mean was 92 .47 and this is divided by the standard deviation which was the standard deviation was this is 29 .99 so this is equal to 65 minus 92 .47.

04:10 And this is divided by 29 .99.

04:14 So that would be negative 0 .91 and 60.

04:20 And what about for z2? this is for the axis equal to 120.

04:24 This is 120 minus 92 .47 divided by 29 .99...

Question

Please give Ace some feedback