# What is the probability that exactly 8 of them are over the age of 65

• MHB
• Crowbarr
In summary: Or, of course, calculate for i= 0, 1, 2, 3, ... , 11 and add.In problem (e) "more than 11" is the same as "12 or more" so you can do the same as (b), calculate the probability for i= 12, 13, 14, 15 and add.In summary, the Agency for Healthcare Research and Quality reported that 53% of people who had coronary bypass surgery in 2008 were over the age of 65. Based on a sample of 15 coronary bypass patients, the probability of exactly 8 of them being over the age of 65 is calculated using the binomial distribution formula. The
Crowbarr
2) The Agency for Healthcare Research and Quality reported that 53% of people who had coronary bypass surgery in 2008 were over the age of 65. Fifteen coronary bypass patients are sampled.

a) What is the probability that exactly 8 of them are over the age of 65?

b) P (less than 10 are over 65) =

c) P (more than 10 are over 65) =

d) P (11 or fewer are over 65) =

e) P ( more than 11 are over 65) =

I am puzzled by this thread. If you have never taken a course in "probability and statistics" where did you get these exercises? If you have, or are now taking such a course, why have you shown no attempt to answer these yourself?

They are all applications of the basic "binomial distribution": if the probability a particular event will result in "a" is p and the probability it will result is "b" is 1- p, the probability that, in n events, it will result in "a" i times and "b" n-i times with probability $$\displaystyle \begin{pmatrix}n \\ I \end{pmatrix}p^i(1- p)^{n-I}$$.

Here, "a" is "a person who had coronary bypass surgery is over 65", p= 0.53, "b" is "a person who had coronary bypass surgery is NOT over 65", and 1- p= 1- 0.53= 0.47. n= 15. [math\begin{pmatrix} n \\ i\/end{pmatrix}[/math] is the "binomial coefficient", $$\displaystyle \frac{n!}{i!(n-i)!}$$.

In problem (a) i= 8.
in problem (b) it is simplest to calculate that for i= 10, 11, 12, 13, 14, and 15, add them (to determine the probability "10 or more are over 65") and subtract from 1. The harder way is to calculate that for i= 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 and add.
In problem (c) you can use the number you got before you subtracted from 1!
In problem (d) "11 or fewer" is the same as "less than 12" so you can do the same as (c), calculate the probability for i= 12, 13, 14, 15 and subtract from 1.

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## What is the probability that exactly 8 of them are over the age of 65?

The probability of exactly 8 out of a group of individuals being over the age of 65 depends on the total number of individuals in the group and the overall percentage of individuals over 65 in the population. Without this information, it is not possible to accurately calculate the probability.

## How do you calculate the probability of exactly 8 individuals being over the age of 65?

To calculate the probability of exactly 8 individuals being over the age of 65, you will need to know the total number of individuals in the group and the percentage of individuals over 65 in the population. Then, you can use the binomial distribution formula to calculate the probability.

## What factors can affect the probability of exactly 8 individuals being over the age of 65?

The probability of exactly 8 individuals being over the age of 65 can be affected by various factors such as the size of the group, the age distribution within the group, and the overall percentage of individuals over 65 in the population. Other factors like genetics, lifestyle, and environmental factors may also play a role.

## Can the probability of exactly 8 individuals being over the age of 65 change over time?

Yes, the probability of exactly 8 individuals being over the age of 65 can change over time. This can happen due to changes in the population demographics, changes in the overall percentage of individuals over 65 in the population, or changes in the age distribution within the group.

## How can the probability of exactly 8 individuals being over the age of 65 be used in scientific research?

The probability of exactly 8 individuals being over the age of 65 can be used in scientific research to make predictions or draw conclusions about a population. It can also be used to test hypotheses or determine the likelihood of certain outcomes in a study. Additionally, it can be used to identify potential risk factors or trends related to aging and health.

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