13th Edition

ISBN: 9780135900826

Author: Triola

Publisher: PEARSON

Concept explainers

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

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Textbook Question

Chapter 5, Problem 9RE

Detecting Fraud The Brooklyn District Attorney’s office analyzed the leading (leftmost) digits of check amounts in order to identify fraud. The leading digit of 1 is expected to occur 30.1% of the time, according to “Benford’s law,’’ which applies in this case. Among 784 checks issued by a suspect company, there were none with amounts that had a leading digit of 1.

a. If there is a 30.1% chance that the leading digit of the check amount is 1, what is the expected number of checks among 784 that should have a leading digit of 1?

b. Assume that groups of 784 checks are randomly selected. Find the mean and standard deviation for the numbers of checks with amounts having a leading digit of 1.

c. Use the results from part (b) and the range rule of thumb to identify the values that are significantly low.

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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Chapter 5, Problem 8RE

Chapter 5, Problem 10RE

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Solution Summary: The author explains that the expected number of checks with the leading digit as 1 is 236 checks and the standard deviation is approximately 12.8 checks.

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