Answered: Let X denote the courtship time for a…

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"†).

(a)

Is it plausible that X is normally distributed?

a)Yes, courtship time is plausibly normally distributed since the mean of X is larger than 100.

b)No, courtship time cannot plausibly be normally distributed. Since X must be non-negative, realistically the interval μ ± 3σ should be entirely non-negative which is not true in this case.

c)Yes, courtship time is plausibly normally distributed. Since X must be non-negative, realistically the interval μ ± 3σ should be entirely non-negative which is true in this case.

d)Yes, courtship time is plausibly normally distributed. Since X must be negative, realistically the interval μ ± 3σ should be entirely negative which is true in this case.

e)No, courtship time cannot plausibly be normally distributed. Since X must be negative, realistically the interval μ ± 3σ should be entirely negative which is not true in this case.

(b)

For a random sample of 60 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 60 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 60? Explain.

A)Yes. According to the guidelines n should be less than 30 in order to apply the central limit theorem.

B)No. According to the guidelines n should be greater than 30 in order to apply the central limit theorem.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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