For an experiment it is randomly collected 40 number of observations and it is not known ex-ante whether this data is normally distributed or not. For this experiment the individual monthly salaries are summed in U.S. dollar terms and found to be 20.000$. For these 40 number of observations the variance term is found to be equal to 6400. Given that set of information, a. Please discuss briefly whether the central limit theorem is appropriate to compare or analyze the m
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
For an experiment it is randomly collected 40 number of observations and it is not known ex-ante
whether this data is
are summed in U.S. dollar terms and found to be 20.000$. For these 40 number of observations the
variance term is found to be equal to 6400. Given that set of information,
a. Please discuss briefly whether the central limit theorem is appropriate to compare or
analyze the
b. Please calculate and interpret the probability that the sample mean will be within
1.5*standard deviation of the mean;
c. Please write down your own question along with an explicit solution related to the
distribution of the sample mean. Here the constraint is that you need to calculate an
interval which corresponds to some probability between 0.05 and 0.20 of this distribution
of the sample mean.
Step by step
Solved in 6 steps with 6 images
