Let X denote the courtship time for a randomly selected female-male pair of mating scorpion flies (time from the beginning of interaction until mating). Suppose the mean value of X is 120 min and the standard deviation of X is 110 min (suggested by data in the article "Should I Stay or Should I Go? Condition- and Status-Dependent Courtship Decisions in the Scorpion Fly Panorpa Cognate"t). A USE SALT (a) Is it plausible that x is normally distributed? O Yes, courtship time is plausibly normally distributed. Since X must be non-negative, realistically the interval u t 3ơ should be entirely non-negative which is true in this case. O No, courtship time cannot plausibly be normally distributed. Since X must be non-negative, realistically the interval u t 30 should be entirely non-negative which is not true in this case. O Yes, courtship time is plausibly normally distributed since the mean of X is larger than 100. O Yes, courtship time is plausibly normally distributed. Since X must be negative, realistically the interval ut 30 should be entirely negative which is true in this case. O No, courtship time cannot plausibly be normally distributed. Since X must be negative, realistically the interval u 2 30 should be entirely negative which is not true in this case. (b) For a random sample of 90 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min? (Round your answer to four decimal places.) (c) For a random sample of 90 such pairs, what is the (approximate) probability that the sample mean courtship time exceeds 150 min? (Round your answer to four decimal places.)