I have questions about R programming. I am confused about question 5 and question 6, especially part d: 1 - pnorm(0.93, 0.932, 0.0448/sqrt(4))

[1] 0.5355726. I used standard deviation on question 4. Could you check my answer?

Thanks,

sample means Frequency WIIIII 0 80 0.920 0.925 0.930 0.935 0.940 xbarHistogram 150 100 Frequency O 0.85 0.90 0.95 xbarsample means Frequency WIIIII 0 80 0.920 0.925 0.930 0.935 0.940 xbar Normal Q-Q Plot Sample Quantiles 0.920 -3 -2 -1 0 2 3 Theoretical QuantilesNormal Q-Q Plot DODO O 0.95 Sample Quantiles 0.90 0.85 O O -3 -2 -1 0 2 3 Theoretical Quantiles4. In problems 4-6, you'll be working with a Beta distribution with parameters shape1=28 and shape2=2 [check out ?dbeta for part a or ?rbeta for part b]. [Note: You do not need to have anywhere Close to a thorough understanding of the Beta distribution in order to do these problems. It is, like the Normal, a continuous distribution that has two parameters and its own suite of built-in R functions. Its support is all values between 0 and 1.] El. b. Plot the probability density function curve of that Beta distribution and describe its shape. Generate a random sample of size n = 4 from that Beta distribution. Find your sample's mean and standard deviation. This Beta distribution has a true mean of pix = 0.9333 and a true standard deviation of ox = 0.0448; your values might be somewhat \"close" to those, but don't expect them to be exact 5. Now generate 1000 samples, each of size n = 4, from a Beta[shape1=28,shape2=2] distribution. El. b. For each of the 1000 samples, calculate the sample mean. Make a histogram of these 1000 sample means, and describe the shape of the histogram. Do you think n = 4 is large enough to use the Central Limit Theorem [CLT] reliably? Conrm with a Normal QQ plot of your sample means. Find the mean and standard deviation of the 1000 sample means. Regardless of your answer to part b, what would you expect the mean and standard deviation of these sample means to be according to the CLT? Regardless of your answer to part b, use the CLT to nd the probability of getting a sample mean above 0.93. How many of your simulated sample means were actually above 0.93? 6. Now generate 1000 samples, each of size n = 200, from a Beta[shape1=28,shape2=2] distribution. [Note: You should be able to reuse most of your code from question 5.] El. b. For each of the 10 00 samples, calculate the sample mean. Make a histogram of these 1000 sample means, and describe the shape of the histogram. Do you think it = 200 is large enough to use the Central Limit Theorem (CLT) reliably? Conrm with a Normal QQ plot of your sample means. Find the mean and standard deviation of the 1000 sample means. Regardless of your answer to part b, what would you expect the mean and standard deviation of these sample means to be according to the CLT? Regardless of your answer to part b, use the CLT to nd the probability of getting a sample mean above 0.93. How many of your simulated sample means were actually above 0.93