The following data represent petal lengths (in cm) forindependent random samples of two species of Iris. Petal length (incm) of Iris virginica: x1; n1 = 35 5.1 5.6 6.2 6.1 5.1 5.5 5.3 5.56.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.44.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.7 5.1 Petal length (in cm) ofIris setosa: x2; n2 = 38 1.6 1.9 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.41.7 1.0 1.7 1.9 1.6 1.4 1.5 1.4 1.2 1.3 1.5 1.3 1.6 1.9 1.4 1.6 1.51.4 1.6 1.2 1.9 1.5 1.6 1.4 1.3 1.7 1.5 1.5 (a) Use a calculatorwith mean and standard deviation keys to calculate x1, s1, x2, ands2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 =(b) Let μ1 be the population mean for x1 and let μ2 be thepopulation mean for x2. Find a 99% confidence interval for μ1 − μ2.(Round your answers to two decimal places.) lower limit upper limit(c) Explain what the confidence interval means in the context ofthis problem. Does the interval consist of numbers that are allpositive? all negative? of different signs? At the 99% level ofconfidence, is the population mean petal length of Iris virginicalonger than that of Iris setosa? Because the interval contains onlypositive numbers, we can say that the mean petal length of Irisvirginica is longer. Because the interval contains only negativenumbers, we can say that the mean petal length of Iris virginica isshorter. Because the interval contains both positive and negativenumbers, we cannot say that the mean petal length of Iris virginicais longer. (d) Which distribution did you use? Why? The Student'st-distribution was used because σ1 and σ2 are unknown. The standardnormal distribution was used because σ1 and σ2 are known. Thestandard normal distribution was used because σ1 and σ2 areunknown. The Student's t-distribution was used because σ1 and σ2are known. Do you need information about the petal lengthdistributions? Explain. Both samples are large, so informationabout the distributions is needed. Both samples are large, soinformation about the distributions is not needed. Both samples aresmall, so information about the distributions is needed. Bothsamples are small, so information about the distributions is notneeded.