Need help figuring these 2 questions out. Thanks.

1. Let X] be a random variable from a distribution with a mean of 8 and a standard deviation of 6 and X2 be a random variable from a distribution with a mean of 7 and a standard deviation of 5. (a)Forindependent samples of sizes m = 3 and m = 6, find the mean and standard deviation of f1 f2. (3 marks) (b) Do X1 and X2 have to be normally distributed for your answer to part (a) to be valid? Explain. (2 marks) (c)Can you conclude that the variable f1 L in part (a) is normally distributed? Explain. (3 marks) (d)$uppose X1 and X2 are normally distributed. determine the percentage of all pairs of independent samples of sizes m = 3 a_nd n_2 = 6 with the property that the difference between the sample means, X1 X2. is between -9 and ii. [5 marks) 2. A study examined the sense of direction of 30 male and 30 female students. After being taken to an unfamiliar wooded park, the students were given some spatial orientation tests, including pointing south. which tested their absolute frame of reference. The students pointed by moving a pointer attached to a 360 protractor. Following are the absolute pointing errors, in degrees. of the participants. Male 13 130 39 33 10 13 68 18 3 l 1 38 23 60 5 9 59 5 86 22 70 58 3 [63'r 15 30 8 20 67 26 19 Female 14 8 20 3 138 128 31 18 35 111 n 109 36 27 32 35 51:38.49 52:48.26 12 27 8 3 80 91 68 66 176 15 (a)Given the statistical summaries, test at the 1% significance level whether males have a better sense of direction than females, on average. (8 marks) (b)What is the P-value of the hypothesis test in part (a)? (2 marks) (c) Obtain and interpret a 98% twosided confidence interval for the difference between the mean absolute pointing errors for males and females. (6 marks) (d) Does the interval in (c) give evidence that on average. males and females differ in the sense of direction? Justify your answer. (2 marks)