Estimated probibility does not match results, why? (galaxies)

[indie452]

Homework Statement

my book states that approx 75% of galaxies in the universe are spirals, but then it says that out of a sample of 14 from the core of a large cluster of galaxies only 3 were found to be spiral.

it was suggested we could use binomial distribution to look at the prob of seeing such small fractions in order to draw a conclusion.

The Attempt at a Solution

i showed binomial prob of seeing 3 was 3.66e-5, and that one would expect 10.5 spirals with a variance of 2.625. clearly this is based on the initial statement of 75% and that is of the whole galaxy, whereas we are looking at a cluster core. so i expect we should have a different prediction.

but is there any other things that can be seen using the binomial distribution to discuss seeing such small fractions?

thanks

 

[anathema]

for any help!



Your question is a very interesting one and it raises some important points about the use of binomial distribution in this scenario. First of all, it is important to note that the initial statement about 75% of galaxies being spirals is an average value for the entire universe. When we look at a small sample of galaxies, such as the 14 from the core of a large cluster, it is possible to see a different distribution of galaxy types.

Using binomial distribution, we can calculate the probability of seeing a certain number of spiral galaxies in a sample of 14, given the overall percentage of spirals in the universe. As you have correctly calculated, the probability of seeing only 3 spiral galaxies in this sample is quite low, indicating that this result is unlikely to occur by chance. However, as you mentioned, this calculation is based on the assumption that the percentage of spirals in the cluster core should be similar to the average percentage in the universe.

There are a few other factors that could affect the distribution of galaxy types in a cluster core, such as the dynamics of the cluster and the environment in which the galaxies are located. It is possible that these factors could lead to a different distribution of galaxy types in the core compared to the rest of the universe. Therefore, it is important to consider these factors when interpreting the results of this sample.

In addition, as you mentioned, the variance of 2.625 indicates that there may be some variation in the number of spiral galaxies that we would expect to see in a sample of 14. This could be due to random chance or other factors that may affect the distribution of galaxy types in a cluster core.

Overall, using binomial distribution can provide valuable insights into the probability of seeing certain results in a sample, but it is important to consider other factors that may affect the distribution of galaxy types in a specific environment. I hope this helps to answer your question and provides some additional considerations for your analysis. Keep up the good work!