Question

According to Benford's law, the probability that the first digit
of the amount of a randomly chosen invoice is a 1 or a 2 is 0.477.
You examine 79 invoices from a vendor and find that 26 have first
digits 1 or 2. If Benford's law holds, the count of 1s and 2s will
have the binomial distribution with *n* = 79 and *p*
= 0.477. Too few 1s and 2s suggests fraud. What is the approximate
probability of 26 or fewer 1s and 2s if the invoices follow
Benford's law? (Use the normal approximation. Round your answer to
four decimal places.)

This answer is NOT = 0.0058677 [since from z table], I asked this question before and the answer is incorrect.

Answer #1

Benford's law, also known as the first‑digit law, represents a
probability distribution of the leading significant digits of
numerical values in a data set. A leading significant digit is the
first occurring non‑zero integer in a number. For example, the
leading significant digit in the number 127127 is 11. Let this
leading significant digit be denoted ?x.
Benford's law notes that the frequencies of ?x in many datasets
are approximated by the probability distribution shown in the
table.
?x
11...

It is a striking fact that the first digits of numbers in
legitimate records often follow a distribution known as
Benford's Law, shown below.
First digit
1
2
3
4
5
6
7
8
9
Proportion
0.285
0.186
0.126
0.084
0.069
0.067
0.034
0.039
0.110
Fake records usually have fewer first digits 1, 2, and 3. What
is the approximate probability, if Benford's Law holds, that among
1153 randomly chosen invoices there are no more than 670 in amounts
with...

It is a striking fact that the first digits of numbers in
legitimate records often follow a distribution known as
Benford's Law, shown below.
First digit
1
2
3
4
5
6
7
8
9
Proportion
0.28
0.152
0.129
0.088
0.05
0.07
0.042
0.035
0.154
Fake records usually have fewer first digits 1, 2, and 3. What
is the approximate probability, if Benford's Law holds, that among
1189 randomly chosen invoices there are no more than 688 in amounts
with...

The first significant digit in any number must be 1, 2, 3, 4,
5, 6, 7, 8, or 9. It was discovered that first digits do not occur
with equal frequency. Probabilities of occurrence to the first
digit in a number are shown in the accompanying table. The
probability distribution is now known as Benford's Law. For
example, the following distribution represents the first digits in
219 allegedly fraudulent checks written to a bogus company by an
employee attempting to...

Benford's Law states that the first nonzero digits of numbers
drawn at random from a large complex data file have the following
probability distribution.† First Nonzero Digit 1 2 3 4 5 6 7 8 9
Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046
Suppose that n = 275 numerical entries were drawn at random from a
large accounting file of a major corporation. The first nonzero
digits were recorded for the sample. First Nonzero Digit 1 2...

The first significant digit in any number must be 1, 2, 3,
4,5, 6, 7, 8, or 9. It was discovered that first digits do not
occur with equal frequency. Probabilities of occurrence to the
first digit in a number are shown in the accompanying table. The
probability distribution is now known as Benford's Law.
Forexample, the following distribution represents the first digits
in 232 allegedly fraudulent checks written to a bogus company by an
employee attempting to embezzle funds...

You might think that if you looked at the first digit in
randomly selected numbers that the distribution would be uniform.
Actually, it is not! Simon Newcomb and later Frank Benford both
discovered that the digits occur according to the following
distribution: (digit, probability)
(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)
The IRS currently uses Benford's Law to detect fraudulent tax data.
Suppose you work for the IRS and are investigating an individual
suspected of embezzling. The first digit of 201 checks to a
supposed company...

ou might think that if you looked at the first digit in randomly
selected numbers that the distribution would be uniform. Actually,
it is not! Simon Newcomb and later Frank Benford both discovered
that the digits occur according to the following distribution:
(digit, probability)
(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)
The IRS currently uses Benford's Law to detect fraudulent tax data.
Suppose you work for the IRS and are investigating an individual
suspected of embezzling. The first digit of 166 checks to a
supposed company...

You might think that if you looked at the first digit in
randomly selected numbers that the distribution would be uniform.
Actually, it is not! Simon Newcomb and later Frank Benford both
discovered that the digits occur according to the following
distribution: (digit, probability)
(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)
The IRS currently uses Benford's Law to detect fraudulent
tax data. Suppose you work for the IRS and are investigating an
individual suspected of embezzling. The first digit of 145 checks
to a supposed company...

Recall that Benford's Law claims that numbers chosen from very
large data files tend to have "1" as the first nonzero digit
disproportionately often. In fact, research has shown that if you
randomly draw a number from a very large data file, the probability
of getting a number with "1" as the leading digit is about 0.301.
Now suppose you are an auditor for a very large corporation. The
revenue report involves millions of numbers in a large computer
file....

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