Lethenote the courtship time for a randomly selected femaleimale pair of mating scorpion flies (time from the beginning of interaction until mating). Suppose the mean value ofX is 120 min and the standard deviation oins 110 min (suggested by data in the article "Should I Stay or Should I Go? Conditions and StatusiDependent Courtship Decisions in the Scorpion Fly Panorpa Cognate"t). USE SA (a) Is it plausible thatX is normally distributed? 0 Yes, courEhip time is plausibly normally distributed. Since X must be negative, realistically the interval p: i 30' should be entirely negative which is true in this case. 0 No, courtship time cannot plausibly be normally distributed. Since X must be noninegative, realistically the interval )1 i 317 should be entirely noninegative which is not true in this case. 0 Yes, courEhip time is plausibly normally distributed since the mean ofX is larger than 100. 0 Yes, courtship time is plausibly normally distributed. Since X must be noninegative, realistically the interval pi t 317 should be entirely noninegative which is true in this case. 0 No, courtship time cannot plausibly be normally distributed. Since X must be negative, realistically the interval p: i 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.) :I (d) Could the probability requested in (b) be calculated from the given information if the sample size were 15 rather than 90? Explain. 0 Yes. According to the guidelines n should be less than 30 in order to apply the central limit theorem. 0 No. According to the guidelines 11 should be greater than 30 in order to apply the central limit theorem