d) (5 points) Are you condent are you that the sample mean in part b] follows aJmLmaL distributions Briey (in two or fewer sentences) explain your rationale. e) (5 points) Select the correct parameters of the distribution described in part d: it? = 0'? = i. 25.33? i. 25.337 ii. 6.54 ii. 6.54 iii. 2.07 iii. 2.07 iv. 16.524 iv. 16.524 4) [20 points] During a game of hopscotch you decide to change the rules up and see how long jumpers can jump without hitting the ropes [in seconds]. We know that this random variable Y is normally distributed with u = 25 and o = 8. a) (3 points) Calculate the probability that a jumper jumps somewhere between 15 and 20 seconds. b) (5 points) You invite n = 15 of your friends to participate and record their times. The following sample statistic are computed from your observations: 17 = 25.337 Calculate the probability that 17 lies within 15 and 20. c) (2 m1 Compare and contrast your responses between parts a] and b] using two or fewer sentences