Suppose you are asked to estimate the 1st quartile (25% point) from a distribution. You are given a sample of size 30: 7.34 8.16 8.69 8.80 8.82 9.28 9.29 9.38 9.43 9.51 9.65 9.78 9.84 9.95 9.98 9.99 10.02 10.05 10.37 10.42 10.52 10.67 10.78 10.87 11.05 11.12 11.19 11.37 11.54 11.92 Given sorted here. a. If I just tell you the data is an id (independent and identically distributed) sample from a distribution, reasoning based on the confidence intervals we construct for the median, hat probability distribution with what parameters should I base the confidence interval on? b. Below is the cumulative distribution for the correct answer to 3a. Construct an approximate 80% confidence interval for the lower quartile (the 25% point 00.0001785821 1 0.0019644030 2 0.0105958707 3 0.0374493257 4 0.0978695996 5 0.2025980742 6 0.3480542890 7 0.5142899631 8 0.6735991507 9 0.8034066369 100.8942718773 11 0.9493417199 12 0.9784063591 13 0.9918208080 14 0.9972504658 15 0.9991810109 16 0.9997843062 17 0.9999499167 18 0.9999897858 19 0.9999981794 20 0.9999997182 210.9999999624 22 0.9999999957 23 0.9999999996 24 1.0000000000 25 1.000 26 1.0000000000