Solved: Approximately 30% of obese patients develop diabetes. If a p…

Approximately 30% of obese patients develop diabetes. If a physician sees 10 patients who are obese, what is the probability that half of them will develop diabetes?




The probability that half of 10 obese patients will develop diabetes can be calculated using the binomial distribution. The binomial distribution is used to model the probability of a certain number of successes in a fixed number of independent Bernoulli trials. In this case, the trials are whether each patient develops diabetes or not, and the probability of success (developing diabetes) is 30%.


To calculate the probability, we need to use the formula for the binomial distribution:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

P(X=k) is the probability of having exactly k successes,
n is the number of trials,
k is the number of successes,
p is the probability of success in each trial,
C(n, k) is the number of combinations of n items taken k at a time.

For this problem, n = 10 (number of patients), k = 5 (half of the patients), and p = 0.30 (probability of a patient developing diabetes).

Using this formula, we can now calculate the probability.

**Calculation Steps**

1. Calculate the number of combinations:
C(n, k) = C(10, 5) = 10! / (5! * (10-5)!)

2. Calculate the probability:
P(X=5) = C(10, 5) * 0.30^5 * (1-0.30)^(10-5)


Utilizing the above formula and calculations, the probability that half of the 10 obese patients will develop diabetes is:

P(X=5) = C(10, 5) * 0.30^5 * (1-0.30)^(10-5)

P(X=5) = 252 * 0.30^5 * 0.70^5

P(X=5) = 252 * 0.00243 * 0.16807

P(X=5) ≈ 0.102518

Therefore, the probability that exactly 5 out of the 10 obese patients will develop diabetes is approximately 0.102518, or 10.25%.

**Conclusion and Implications**

In conclusion, using the binomial distribution, we have determined that the probability of exactly half of the 10 obese patients developing diabetes is approximately 0.102518, or 10.25%. This calculated probability is based on the assumption that the probability of developing diabetes remains constant for each patient and that the patients are independent of each other.

Understanding these probabilities can help physicians, researchers, and policymakers in assessing the likelihood of diabetes development in obese patients. It can also aid in making informed decisions about the allocation of resources for prevention and treatment interventions.

It is essential to note that individual cases may not always align with the calculated probability due to inherent variations. Nonetheless, the use of probability and statistical modeling provides a valuable framework for decision-making and understanding the likelihood of specific outcomes.

Calculate the price
Make an order in advance and get the best price
Pages (550 words)
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with TOP USA homework
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Customer reviews in total
Current satisfaction rate
3 pages
Average paper length
Customers referred by a friend
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat
error: Content is protected !!