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Category: Calculus and Above
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Experience:  B.S. in Civil Engineering
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# 1. Glucose levels in patients free of diabetes are assumed

### Resolved Question:

1. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean of 120 and a standard deviation of 16.
a) What proportion of patients have glucose levels exceeding 115?
b) If a patient has a glucose level of 140, what percentile is this?
c) What is the probability that the mean glucose level exceeds 115 in a sample of 12 patients?
2. The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.
25 27 31 33 26 28 38 41 24 32 35 40
a) Compute the mean BMI
b) Compute the standard deviation of BMI
c) Compute the median BMI
d) Compute Q1 and Q3
e) Are there outliers in the distribution of BMI (justify your answer)?
3. The following table shows the numbers of patients classified as underweight, normal weight, overweight and obese according to their diabetes status.
Underweight
Normal Weight
Overweight
Obese
Diabetes
8
34
65
43
No Diabetes
12
85
93
40
If a patient is selected at random,
a) What is the probability that they are overweight?
b) What is the probability that they are obese and diabetic?
c) What proportion of the diabetics are obese?
d) What proportion of normal weight patients are not diabetic?
e) What proportion of patients are normal weight or underweight?
4. Approximately 30% of obese patients develop diabetes. If a physician sees 10 patients who are obese,
a) What is the probability that half of them will develop diabetes?
b) What is the probability that none will develop diabetes?
c) How many would you expect to develop diabetes?
Submitted: 2 years ago.
Category: Calculus and Above
Expert:  Ryan replied 2 years ago.
Hi,

Thank you for your questions. I'll be happy to help you with these. I'll get started on them immediately and will have the solutions posted for you as soon as possible.

Thanks,

Ryan
Customer: replied 2 years ago.

Expert:  Ryan replied 2 years ago.
Hi Mary,

It will probably take 45 minutes or so to get it all typed up, maybe a little longer. You should receive an email notification when the answers are posted.

Ryan
Customer: replied 2 years ago.

Thank you.

Expert:  Ryan replied 2 years ago.
Hi Mary,

Here are the solutions:

Stats

(Clicking on the link above will open a new page where you can choose to either view or download the solution file.)

Thanks,

Ryan
Customer: replied 2 years ago.

Can you provide how this would look on an Excel document?

Expert:  Ryan replied 2 years ago.
Hi Mary,

Are you required to submit this as an Excel document?

The reason I ask is that using Excel will do absolutely nothing to enhance this in any way. In fact, it will actually make it harder to read and understand.

Ryan
Customer: replied 2 years ago.

Unfortunately yes.

I also have these additional questions. I can add another a payment.

Or do I need to resubmit another ask question?

A new non-invasive screening test is proposed that is claimed to be able to identify patients with impaired glucose tolerance based on a battery of questions related to health behaviors. The new test is given to 75 patients. Based on each patient’s responses to the questions they are classified as positive or negative for impaired glucose tolerance. Each patient also submits a blood sample and their glucose tolerance status is determined. The results are tabulated below.
Screening Test
Impaired Glucose Tolerance
Not Impaired
Positive
17
13
Negative
8
37
a) What is the sensitivity of the screening test?
b) What is the false positive fraction of the screening test?
6. BMI in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2.
a) A BMI between 25 and 30 is considered overweight. What proportion of children are overweight?
b) A BMI of 30 or more is considered obese. What proportion of children are obese?
c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?
7. A national survey is conducted to assess the association between hypertension and stroke in persons over 55 years of age. Development of stroke was monitored over a 5 year follow-up period. The data are summarized below and the numbers are in millions.
Developed Stroke
Did not Develop Stroke
Hypertension
12
37
No Hypertension
4
26
a) Compute the incidence of stroke in persons over 55 years of age
b) Compute the relative risk of stroke comparing hypertensive to non-hypertensive persons
c) Compute the odds ratio of stroke comparing hypertensive to non-hypertensive persons
8. Answer True or False to each of the following
a) If there are outliers, then the mean will be greater than the median.
b) The 90th percentile of the standard normal distribution is 1.645.
c) The mean is the 50th percentile of any normal distribution.
d) The mean is a better measure of location when there are no outliers.

Expert:  Ryan replied 2 years ago.
Hi,

I can put the previous answers into Excel, but it will take some time, and it won't be as pretty.

I would suggest that you post these additional questions as a new question so that another expert can work on them while I'm moving all the previous work to Excel.

Thanks,

Ryan
Customer: replied 2 years ago.

Thank you.

Expert:  Ryan replied 2 years ago.
Hi Mary,

Here is an Excel file with the previous solutions:

Stats(Excel)

Thanks,

Ryan
Ryan, Engineer
Satisfied Customers: 8597
Experience: B.S. in Civil Engineering

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