please give me solution in detail.

( 30 points) light bulbs are tested for their luminance, with the intensity of brightness desired to be within a certain range. Random samples of five bulbs are chosen from the output, and the luminance is measured. The sample mean X and the standard deviations are found. After 30 samples, the following summary in formation is obtained: i=130Xi=2550,i=13si=195 The specifications are 9015 lumens. a. (5 points) Find the Xands-chartcontrollimits.. b. (5 points) Assuming that the process is in control, estimate the process mean and process standard deviation c. (10 points) Comment on the ablity of the process to meet specifications. What proportion of the output is nonconforming? d. (10 points) If the process mean is moved to 90 lumens, what proportion of output will be nonconforming? What sugggestions would you make to improve the performance of the process