Please show and explain the steps! 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 Cognata“).### (a) Is it plausible that \( X \) is normally distributed?- ○ Yes, courtship time is plausibly normally distributed. Since \( X \) must be non-negative, realistically the interval \( \mu \pm 3\sigma \) should be entirely non-negative which is true in this case.- ○ No, courtship time cannot plausibly be normally distributed. Since \( X \) must be non-negative, realistically the interval \( \mu \pm 3\sigma \) should be entirely non-negative which is not true in this case.- ○ Yes, courtship time is plausibly normally distributed since the mean of \( X \) is larger than 100.- ○ Yes, courtship time is plausibly normally distributed. Since \( X \) must be negative, realistically the interval \( \mu \pm 3\sigma \) should be entirely negative which is true in this case.- ○ No, courtship time cannot plausibly be normally distributed. Since \( X \) must be negative, realistically the interval \( \mu \pm 3\sigma \) 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.)\[ \text{Box for answer} \]### (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.)\[ \text{Box for answer} \]### (d) Could the probability requested in (b) be calculated from the given information if the sample size were 15 rather than 90? Explain.- ○ Yes. According to the guidelines \( n \) should be less than 30 in order to apply

The random variable denotes the courtship time for the scorpion. Mean is 120 and standard deviation…

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"r). 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 ut 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 a t 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 : 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.) (d) Could the probability requested in (b) be calculated from the given information if the sample size were 15 rather than 90? Explain. O Yes. According to the guidelines n should be less than 30 in order to apply the central limit theorem. O No. According to the guidelines n should be greater than 30 in order to apply the central limit theorem.

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"r). 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 ut 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 a t 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 : 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.) (d) Could the probability requested in (b) be calculated from the given information if the sample size were 15 rather than 90? Explain. O Yes. According to the guidelines n should be less than 30 in order to apply the central limit theorem. O No. According to the guidelines n should be greater than 30 in order to apply the central limit theorem.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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