Hi, I have a question about using R studio in statistics. How to write codes for this question? Thanks!

Problem 2: A normal approximation of the sampling distribution of proportions That wasn't easy at all. was It? You had to calculate and store the whole probability distribution. sort it In order of descending probabilities. calculate the cumulative probabilityfro mthe most to least likely outcomes. and isolate those cases that account for 95% ofthe most probable outcomes. As It turns out, Identifying the range of highest-probability outcomes for a probability distribution Is never easy when the distribution is discrete and/or asymmetrical. Consequently. we often prefer to work with a normal approximation of the sampling distribution of proportions. p \".5 Nomalup. SE... ). To do so. we need to identify the mean a... as well as the standard deviation which we give a special name ("standard error'j whenever we are using the normal distribution to model sampling distributions of statistics, in this case the standard error of proportions SE... In this case. a #11:\" $5., = [nun1r) With a normal distribution. we can easily identify an Interval that contains the 95% most probability outcomes by identifying {a} a lower value of p to the left of which 2. 5% ofthe area under the curve falls and lb] an upper value of p to the right of which 2.5% of the area under the curve falls. The expression lip i 1.963153, can be used fortnls operation. where $1.96 Is the interval for the standard normal distribution within which the 95% most probable outcomes Ila. {A} In the code chunI-c below. identify the interval containing the 95% most probable outcomes assuming {it = 0.75.11 = 30}. Do the same for {.il.' = 0.45. l! = 60}. Compare these to the exact results you identified In Question 1 based on sorting the binomial distribution from mostto least probable outcomes. iii'i'ite one sentence Identifying the boundaries of the interveloasedon {it = 0.75. it = 30}. Write a second sentence ldentfiylng the boundaries of the interval bassoon {it = 0.45. h. = 60}. Write one sentence each loreach of these two intervals. comparing them to the intervals you calculated in Question 1. [B] While I. = 11.96 is useful If we are interested in Identifying the 95% most probable outcomes. what If we wish to identify an interval for a different percentage? We can use the quantlle function in Ft to do so. as in the following code chunk for 90%: HostProhProp - 0.9 [teilCDPe - cltl-KoetPL-ohPL-opll, 1-[1-noetProbPrcpil2n 'H [1] 0.05 0.95 qnormt p - teilCDFB 1\