Consider the probability distribution for number of children in local families.xP(x)00.0310.1120.3630.3340.17 Find the mean number of children in local families ["", "", "", "", ""] Find the standard deviation of the number of children in local families ["", "", "", "", ""] Would 4 children be considered a significantly high number of children? ["", "", "", "", ""]

The table shows the probability distribution for number of children in local families.1. The mean number of children in local families is, Ex=∑xPx=0×0.03+1×0.11+2×0.36+3×0.33+4×0.17=0+0.11+0.72+0.99+0.68=2.5 Thus, the mean number of children in local families is 2.5.2. The expected value of x2 is, Ex2=∑x2Px=02×0.03+12×0.11+22×0.36+32×0.33+42×0.17=0+0.11+1.44+2.97+2.72=7.24 The standard deviation of the number of children in local families is, SD=Ex2-Ex2=7.24-2.52=7.24-6.25=0.99=0.995 Thus, the standard deviation of the number of children in local families is 0.995.3. The probability of having four children is less than the probability having 2 children and probability of having 3 children indicating that the having 4 children should not be considered as significantly high number of children. Correct Answer: No.

Answered: Consider the probability distribution…

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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Consider the probability distribution for number of children in local families.

x	P(x)
0	0.03
1	0.11
2	0.36
3	0.33
4	0.17

Find the mean number of children in local families ["", "", "", "", ""]
Find the standard deviation of the number of children in local families ["", "", "", "", ""]
Would 4 children be considered a significantly high number of children? ["", "", "", "", ""]

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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