please use R or by hand to solve this question and post the code.

Problem # 2. Suppose that a quality characteristic has a normal distribution with specification limits at USL=100 and LSL=90. A random sample of 30 parts results in i=97 and S=l.6. (a) Find a point estimate of Cp. Find a 95% confidence interval for CF. (b) Test the hypothesis that the C p is not capable. (c) Find a point estimate of C pk. Find a 95% confidence interval for C pk. (d) Consider the following approximate confidence interval for C Pk A 1 n l Cpk[1_Za/2 202-1)] 5 Cpk s (L'J,J,C[1+zw,2 2014)] How good is the approximation compared to part (c)