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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 th "Should I Stay or Should I Go? Condition- and Status-Dependent Courtship Decisions in the Scorpion Fly Panorpa Cognate"*). 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 30 should be entirely non-negative wvhich is true in this case. O No, courtship time cannot plausibly be normally distributed. Since X must be non-negative, realistically the interval at 30 should be entirely non-negative which is not true in this case. O Yes, courtship time is plausibly normally distributed. Since X must be negative, realistically the interval at 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. O Yes, courtship time is plausibly normally distributed since the mean of X is larger than 100. (b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 115 min and 135 min? (Round your answer to four decimal places.) (c) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time exceeds 160 min? (Round your answer to four decimal places.)

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 th "Should I Stay or Should I Go? Condition- and Status-Dependent Courtship Decisions in the Scorpion Fly Panorpa Cognate"*). 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 30 should be entirely non-negative wvhich is true in this case. O No, courtship time cannot plausibly be normally distributed. Since X must be non-negative, realistically the interval at 30 should be entirely non-negative which is not true in this case. O Yes, courtship time is plausibly normally distributed. Since X must be negative, realistically the interval at 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. O Yes, courtship time is plausibly normally distributed since the mean of X is larger than 100. (b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 115 min and 135 min? (Round your answer to four decimal places.) (c) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time exceeds 160 min? (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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). In 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 µ ± 30 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 ± 30 should be entirely non-negative which is not true in this case. O Yes, courtship time is plausibly normally distributed. Since X must be negative, realistically the interval u ± 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. O Yes, courtship time is plausibly normally distributed since the mean of X is larger than 100. (b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 115 min and 135 min? (Round your answer to four decimal places.) (c) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time exceeds 160 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 50? Explain. O No. According to the guidelines n should be greater than 30 in order to apply the central limit theorem. O Yes. According to the guidelines n should be less than 30 in order to apply the central limit theorem.
Transcribed Image Text: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). In 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 µ ± 30 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 ± 30 should be entirely non-negative which is not true in this case. O Yes, courtship time is plausibly normally distributed. Since X must be negative, realistically the interval u ± 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. O Yes, courtship time is plausibly normally distributed since the mean of X is larger than 100. (b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 115 min and 135 min? (Round your answer to four decimal places.) (c) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time exceeds 160 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 50? Explain. O No. According to the guidelines n should be greater than 30 in order to apply the central limit theorem. O Yes. According to the guidelines n should be less than 30 in order to apply the central limit theorem.
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