0 Question 6 v In this problem, we explore the relationship between the Central Limit Theorem (CLT) and the Normal Distribution. Suppose that exam scores are normally distributed with a mean of 60 and standard deviation of 8. So the population distribution looks like this: i i | i i 28 36 44 52 60 68 F6 84 92 Emu: Score Now, according to the CLT, if we take repeated samples from this population and compute the sample mean [22) for each one, the resulting sampling distribution will also be normally distributed with the same mean but a smaller standard deviation. a. Suppose we take repeated samples of n = 4 exam scores. Find the mean and standard deviation of the sampling distribution. Round to one decimal if needed. The mean will be p5 = p = 0' The standard deviation will be 0'5 2 = ,5 Thus, the graph of the sampling distribution will be: .Mcm: Emu: Score (is = 4) Note how the scale of the second graph is smaller that of the first. So the second graph is actually more narrow than the first. Now let's compute some probabilities. b. Suppose that we choose one single exam from the population. Find the probability that this score will be less than 68. Round to four decimals. 28 36 44 52 60 68 F6 84 92 Exam Scare Since this problem involves only one value, not the mean of n values, we do not need to use the CLT. So we just use the normalcdf {TI} or NormalDist.cdf [ClassCalc) command to find the red shaded area. P(X