Answered: The random variable X is the crew size…

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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The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.

x	2	4	5	6	7	8
P(X=x)	0.021	0.034	0.265	0.248	0.427	0.005

a. Find and interpret the mean of the random variable.

μ=_____

(Round to three decimal places as needed.)

Interpret the mean. Select the correct choice below and fill in the answer box to complete your choice.

A. The average number of persons in a shuttle crew is_____person(s).

B. The most common number of persons in a shuttle crew is_____person(s).

b. Obtain the standard deviation of the random variable.

σ=______

(Round to three decimal places as needed.)

c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below.

The mean is____.The one-standard-deviation interval is___,___the two-standard-deviation interval is___,___and the three-standard-deviation interval is____,____.

(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)

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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