Problem 3(40 points)Assume IQs of all people have mean 100 and standard deviation 15 (notice here th

Problem 3(40 points)Assume IQs of all people have mean 100 and standard deviation 15 (notice here the IQ is notnecessarily Normal Distributed).I.Write out what is the Central Limit Theorem. (10’)(Hint: what is the distribution of sampleaverage? including the name of distribution and its parameter)II. We randomly choose 40 people as our sample, then what is the sampling distribution ofaverage IQ of our sample? (10’)III. What is the probability that the average IQ of our sample higher than 105? (10’)IV. What is the probability that the average IQ of our sample lower than 95? (10’)