Please Show how to do in R with the code

4. (20 pts) This problem appeared in Montgomery 7th edition, but it does not appear in the 8th edition, so here it is. The table below contains 20 observations on cycles to failure of aluminum test coupons subjected to repeated alternating stress of 15,000 psi at 20 cycles per second. Cycles to failure of test coupons 8078 1891 13912 3407 6168 15504 1893 12551 6861 1334 9438 6227 2562 2074 6770 7971 17081 9245 19041 21997 (a) Fit this data to a Normal distribution and to a Lognormal distribution by estimating the param- eters of the Normal and the Lognormal distributions. (b) Check the quality of the fit by making a QQ plot (for each distribution). Include the plots with your homework. (c) Using your estimated parameters (for each distribution), find the probability that an aluminum test coupon fails before 6000 cycles. (d) Based on the plots, which distribution seems to be the best fit for the cycles to failure? 4. (20 pts) This problem appeared in Montgomery 7th edition, but it does not appear in the 8th edition, so here it is. The table below contains 20 observations on cycles to failure of aluminum test coupons subjected to repeated alternating stress of 15,000 psi at 20 cycles per second. Cycles to failure of test coupons 8078 1891 13912 3407 6168 15504 1893 12551 6861 1334 9438 6227 2562 2074 6770 7971 17081 9245 19041 21997 (a) Fit this data to a Normal distribution and to a Lognormal distribution by estimating the param- eters of the Normal and the Lognormal distributions. (b) Check the quality of the fit by making a QQ plot (for each distribution). Include the plots with your homework. (c) Using your estimated parameters (for each distribution), find the probability that an aluminum test coupon fails before 6000 cycles. (d) Based on the plots, which distribution seems to be the best fit for the cycles to failure