Problem10. There are total 100 senator. Consider the below table Democrat Republican Independent Total Male 35 43 2 80 Female 16 4 0 20 Total 51 47 2 100 a) If we randomly select one senator, What is the probability that a male select? Show all your steps. (2 points) b) If we randomly select one senator, what is the probability that a female is selected? Show all your steps. (2 points) c) If you randomly select one senator what is the probability that a female and Democrat is selected? Show all your steps. (2 points) d) If you randomly select one senator what is the probability of selecting an independent given that it was a male? Show all your steps. (2 points) Problem 6. Consider the below table Class Frequency 0-50 10 51-101 20 102-152 30 153-203 40 204-254 50 6a) Find the mean? Show all your steps. Round off mean to only 2 decimal places. (2 points) 6b) Find the variance? Show all your steps. Use the mean you found in the above problem 6a). Round off to two decimal places, your nal answer for variance. (6 points) 6c) Find the standard deviation? Show all your steps. Round off to two decimal places, your nal answer for standard deviation. (4 points) Problem 7. For the set of data below, 5, 3, 8, 6, 1, -10, 3, 9, 7, 4, 2 7a) Determine the 5 point summaries? Show all your steps. (6 points) 7b) Construct the box and whisker plot? Show all your steps. (4 points) 7c) Find if there are any outliers? Justify your answer. Show all your steps. (4 points) Problem 8. An emergency service wishes to determine whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data are shown. Temperature x No. Of calls y 25 7 10 4 27 8 30 10 33 11 8a) Find the correlation coefficient r? Show all your steps. Do not round off. (6 points) 8b) Find the regression equation? Show all your steps. (10 points)Problem 9. You toss a fair coin 4 times 9a) Write the probability experiment? (1 point) 9b) Write the sample Space for the above probability experiment? Show all your steps. (3) 9c) What is the probability of getting at most 2 heads? Show all your steps. (2 points) 9d) What is the probability of getting at least 3 tails? Show all your steps. (2 points)