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,

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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 20.000S. 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 mean value of this sample within certain intervals;
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.
Transcribed Image Text: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 20.000S. 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 mean value of this sample within certain intervals; 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.
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