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 Xis 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"(Animal Behavior, 2009: 491-497)).

a. Is it plausible that X is normally distributed?
b. For a random sample of 50 such pairs, what is the (approximate)
probability that the sample mean courtship time is between 100
min and 125 min?

c. For a random sample of 50 such pairs, what is the (approximate)
probability that the total courtship time exceeds 150 hr?
d. Could the probability requested in (b) be calculated from the
given information if the sample size were 15 rather than 50?
Explain.

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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