According to the stock index, the return from January 2014 to December 2014 shows the average of 7% with standard deviation of 2.5%. 1) According to the Central Limit Theorem (CLT), what the sample mean distribution if we randomly pick 25 stocks? 2) What is the probability that the sample mean is higher than 8% if we randomly select 25 stocks? 3) What is the probability that the sample mean is lower than 6.5% if we randomly select 100 stocks? 4) Suppose the population mean is unknown, but we know the population standard deviation is 2.5. What is the 95% confidence interval of population mean if the sample mean is 7.2$ and the sample standard deviation is 3% from randomly selected 25 stocks?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
According to the stock index, the return from January 2014 to December 2014 shows the average of 7% with standard deviation of 2.5%.
1) According to the Central Limit Theorem (CLT), what the sample
2) What is the
3) What is the probability that the sample mean is lower than 6.5% if we randomly select 100 stocks?
4) Suppose the population mean is unknown, but we know the population standard deviation is 2.5. What is the 95% confidence interval of population mean if the sample mean is 7.2$ and the sample standard deviation is 3% from randomly selected 25 stocks?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
