In a study of data derived from a variety of natural phenomena, F. A. Benford formulated an empirical law regarding the frequency of occurrence of the first digit ? in a set of numbers. Researchers have recognized Benford’s law, also known as the first-digits law, as an important tool in data analysis for diverse arenas such as forensic accounting, online social networking, climate modeling, and gene sequencing. For specific data sets, Benford observed that the frequencies of occurrence of ? were approximated by the probability distribution shown in the table. ? 1 2 3 4 5 6 7 8 9 ?(?) .301 .176 .125 .097 .079 .067 .058 .051 .046 Use Benford’s Law to find ?(?<3) and ?(?>4) . Express each result as a decimal rounded to three places. ?(?<3)= ?(?>4) =
In a study of data derived from a variety of natural phenomena, F. A. Benford formulated an empirical law regarding the frequency of occurrence of the first digit ? in a set of numbers. Researchers have recognized Benford’s law, also known as the first-digits law, as an important tool in data analysis for diverse arenas such as forensic accounting, online social networking, climate modeling, and gene sequencing.
For specific data sets, Benford observed that the frequencies of occurrence of ? were approximated by the probability distribution shown in the table.
? 1 2 3 4 5 6 7 8 9
?(?) .301 .176 .125 .097 .079 .067 .058 .051 .046
Use Benford’s Law to find ?(?<3) and ?(?>4) . Express each result as a decimal rounded to three places.
?(?<3)=
?(?>4) =
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