Problem 2. (30 points) Based on the outputs from R using PCA for the world temperature data, answer the following questions. (see the pdf file, Output from R) a A principal component analysis is performed on the observed data. Based on the output, what percentage of the total vari- ation is explained by the 1st principal component? b Assume the first original variable "HIGH" is normal. One makes the statement that the average HIGH is greater than 75. Test if the statement can be supported by the sample. Hint: consider test Ho : HIGH < 75 against H, : WHIGH > 75 (5 points)