A company that rents DVDs from vending machines in grocery stores has developed the following probability distribution for the random variable X = the number of DVDs a customer rents per visit to a machine. X1234P(X)0.50.30.10.1 a) Find and interpret the mean (expected value) of X.b) Find and interpret the standard deviation of X.c) What is the probability that a customer rents more than 2 DVDs per visit to a machine?

Given that X 1 2 3 4 P(X) 0.5 0.3 0.1 0.1 1a) Mean of X: X 1 2 3 4 P(X) 0.5 0.3…

Answered: A company that rents DVDs from vending…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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A company that rents DVDs from vending machines in grocery stores has developed the following probability distribution for the random variable X = the number of DVDs a customer rents per visit to a machine.

X	1	2	3	4
P(X)	0.5	0.3	0.1	0.1

a) Find and interpret the mean (expected value) of X.

b) Find and interpret the standard deviation of X.

c) What is the probability that a customer rents more than 2 DVDs per visit to a machine?

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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A company that rents DVDs from vending machines in grocery stores has developed the following probability distribution for the random variable X = the number of DVDs a customer rents per visit to a machine. X 1 2 3 4 P(X) 0.5 0.3 0.1 0.1 a) Find and interpret the mean (expected value) of X.