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# Simulated data is frequently used in economic research. An example of how a simulated data set may be constructed is through using a random number...

Simulated data is frequently used in economic research. An example of how a simulated data set may be constructed is through using a random number generator. Consider when random numbers between 0 and 1 are generated, with each generated number having four decimal places. Now decide that a sample of 500,000 randomly generated numbers is to be selected. These 500,000 numbers will form what is called a data set.

If the mean of distribution of the individual random numbers between 0 and 1 is 0.5 and the variance 1/12, calculate:

a) The probability that a random sample of 500,000 numbers (a data set) will have a sample mean no larger than 0.5005. Answer to 4 decimal places:

b) Using the probability from part a, if 1,000 data sets include 500,000 random numbers, how many of these data sets would be expected to have a sample mean of no larger than 0.5005 (calculate to the nearest whole number)? Answer: