TSTA602 Assignment 1April 25, 2020Instructions. This assignment has a total of 20 marks and worth 20% of the finalgrade of TSTA602. The detailed marks allocation are provided at the beginningof each...

TSTA602 Assignment 1April 25, 2020Instructions. This assignment has a total of 20 marks and worth 20% of the finalgrade of TSTA602. The detailed marks allocation are provided at the beginningof each question. You are encouraged to discuss the assignment with your peers,but must write down your own solution. Unless otherwise specified, please calculateyour answer to four decimal places, if your answer is not exact and you have toapproximate your result. This assignment is due at 5pm on Friday of Week 6(8th May, 2020). Please submit your assignment before the deadline.Scenario. Bank X provides home loan service to their retail customers and chargea interest rate for their service. Due to market fluctuations, Bank X only offersfloating interest rate (FIR) for their home loan customers. A friend of you whoworks as a banker at Bank X told you that the average yearly FIR in the last thirtyyears follows a Normal distribution with mean 3.2% (i.e., μ = 0.032) and standarddeviation 0.04 (i.e.,  = 0.04). In addition, a sample of size 10 (drawn from N(0.032,0.0016)) is available to you which has been summaried in the table below-0.021 0.029 -0.009 -0.002 0.002 -0.006 0.006 -0.064 0.023 0.031Table 1: A sample of FIRYour friend seek help from you to use your knowledge from TSTA602 to assistBank X to do the following data analysis. Please write a report to answer all thefollowing questions.(a). (3 marks) calculate (mannually) the sample mean, and sample standard de-viation for the sample in Table 1.(b). (4 marks) if we draw samples of sizes 10 many times and form a distribution ofsample mean, state the distribution of the sample mean and provide the reasonfor your conclusion; calculate the mean of the sample means and its standarddeviation.(c). (5 marks) based on (b), find the probability that the sample mean is smallerthan 0.02. Please keep two decimal places in the calculation of standardization.(d). (2 marks) if the sample mean from (a) is your observed value, calculate the95% confidence interval for the sample mean.(e). (2 marks) An outlier is a data point outside the interval [Q1 − 1.5IQR,Q3 +1.5IQR], where Q1 and Q3 are first and third quartile respectively, and IQR1is the interquartile range. Explain whether there is any outlier appears in thesample in Table 1? You can calculate Q1 and Q3, and IQR using R (in Rstudio).(f). (4 marks) Use R (in Rstudio) to generate 1,000,000 samples of size 10 fromN(0.032, 0.0016) (please set the seed equals to 602), compute the sample meanfor each of these samples, draw a histgram (set the frequency parameter toFALSE) for these sample means and add a density curve to the histgram. Pleaseprovide the histgram with the density curve here and attach your R code asappendix.2