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

  • Thread starter Thread starter Crowbarr
  • Start date Start date
  • Tags Tags
    Age Probability
AI Thread Summary
The discussion focuses on calculating probabilities using the binomial distribution for coronary bypass patients, specifically regarding the age of patients over 65. It cites that 53% of coronary bypass surgery patients were over 65 in 2008 and involves a sample of 15 patients. The calculations for various scenarios, such as exactly 8 patients over 65 and probabilities for fewer or more than 10, are explained using the binomial formula. The thread also questions the participants' understanding of probability concepts, suggesting they should attempt to solve the problems independently. Overall, the emphasis is on applying binomial distribution principles to derive the required probabilities.
Crowbarr
Messages
1
Reaction score
0
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) =
 
Mathematics news on Phys.org
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 [math]\begin{pmatrix}n \\ I \end{pmatrix}p^i(1- p)^{n-I}[/math].

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", [math]\frac{n!}{i!(n-i)!}[/math].

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.
 
Last edited by a moderator:
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top