Answered: blue balls and 3 green balls. Two balls…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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A box contains 4 blue balls and 3 green balls. Two balls are drawn consecutively without replacement. assume that the random variable Y defines the number of blue balls?1.Construct a probability distribution for Y. 2.what is the mean of the distribution?Interpret the result. 3.Compute the variance and standard deviation of the distribution.

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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As per the bartleby guidelines for more than two parts only two has to be solved. Please upload the other parts separately.

The number of blue balls in the box is 4 and the number of green balls in the box is 3.

It is given that two balls are drawn consecutively without replacement ,

The probabilities of the events are :

Events	Probability
GG	$\frac{3}{7} \times \frac{2}{6} = \frac{1}{7}$
GB	$\frac{3}{7} \times \frac{4}{6} = \frac{2}{7}$
BG	$\frac{4}{7} \times \frac{3}{6} = \frac{2}{7}$
BB	$\frac{4}{7} \times \frac{3}{6} = \frac{2}{7}$

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