Find the solution to the following problems.

Which of the following statements regarding the Central Limit Theorem is FALSE? (a) The Central Limit Theorem assumes that the sample drawn from the population consists of i.i.d random variables. (b) The Central Limit Theorem states that, for large sample sizes, the sample mean has an approximately normal distribution. (c) The Central Limit Theorem states that, for large sample sizes, the random variable YLE has a H standard normal distribution where T, ,u,, and or are the sample mean, population mean, and population standard deviation respectively. ((1) The Central Limit Theorem assumes that the distribution of the population from which the sample is drawn must be normal. [UNIT 3] HW: Normal Distributions and The Cent Limit Theorem (CLT) Score: 65.54/100 9/14 answered Done . Question 14 0/10 pts 03 Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.8-in and a standard deviation of 0.9-in. In what range would you expect to find the middle 98% of most head breadths? Between and If you were to draw samples of size 38 from this population, in what range would you expect to find the middle 98% of most averages for the breadths of male heads in the sample? Between and Enter your answers as numbers. Your answers should be accurate to 2 decimal places. Submit QuestionProblem 1: A Central Limit Theorem Simulation Here we will perform a Central Limit Theorem simulation similar to the ones done in class. That is: . Pick a distribution (that was not presented in class) . Justify that the distribution will abide by the central limit theorem . Find a parameter set and value for / where we can see that the central limit theorem clearly applies . Find a parameter set and value for / where we can see that the central limit theorem does not apply . Code must be submitted (preferably in R, but MATLAB, Python, ForTran, and C++ will also be accepted).A sample of size n is taken from a population with an unknown distribution, with mean // and standard deviation O. Which of the following statements about the sample mean distribution is true? Select one: a. Using the Central Limit Theorem, Xexactly followsX- Nu, n b. without Using the Central Limit Theorem, X approximately followsX - N H,- n O C. Using the Central Limit Theorem, X approximately followsX - Nu.- n O d. without Using the Central Limit Theorem, 02 Xexactly followsX - Nu