The vast majority of the world uses a 95 confidence in build

-The vast majority of the world uses a 95% confidence in building confidence intervals. Give your opinion on why 95% confidence is so commonplace. Justify your response.

Solution

From the standard normal distribution, the probability that a value will lie within one standard deviation from the mean is 68%. And the probability that a value will lie within two standard deviations from the mean is 95%.

Now, 68% is way too low a value to consider. 68% or nearly 7 in 10 is nearly not a good enough confidence level.

On the other hand, 95%, which comes out to 19 in 20 is quite a good confidence interval.

When performing statistical calculations, there will be many situations where we would have to sample a population that is way larger than 20. In this world of big data, the sample size can exceed even a million.

Now, when we consider say a sample of 1,000,000, using the 95% confidence interval, we get that 95% of 1000000 = 950000 values lie within two standard deviations of the mean of the dataset.

And in such a case if the standard deviation is low, i.e, if the data entries lie very very close to each other, then, a 95% confidence interval will yield even more accurate results. In this world of increasing accuracy and precision, it is true that in most experiments, when the sample size is very very large, and the standard deviation is low, a 95% confidence interval is enough to account for nearly all of the dats entries.

Therefore, a 95% confidence nterval is commonplace in today\'s world.