document.write( "Question 1192724: A math professor finds that when he schedules an office hour for student help, an average of 1.5 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 6. \n" ); document.write( "
Algebra.Com's Answer #824628 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "This uses the Poisson Distribution.
\n" ); document.write( "More info can be found here:
\n" ); document.write( "https://online.stat.psu.edu/stat414/book/export/html/678\r
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\n" ); document.write( "\n" ); document.write( "\"lambda\" = greek letter lambda
\n" ); document.write( "lambda = 1.5 = average number of arrivals per hour\r
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\n" ); document.write( "\n" ); document.write( "P(x) = probability of having exactly x arrivals (x = 0, x = 1, x = 2, ...)
\n" ); document.write( "P(x) = \"%28e%5E%28-lambda%29%2Alambda%5Ex%29%2F%28x%21%29\"
\n" ); document.write( "The exclamation mark indicates factorial. Example: 5! = 5*4*3*2*1 = 120.
\n" ); document.write( "The 'e' refers to the special constant e = 2.718...\r
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\n" ); document.write( "\n" ); document.write( "Plug in lambda = 1.5 and x = 6
\n" ); document.write( "P(x) = \"%28e%5E%28-lambda%29%2Alambda%5Ex%29%2F%28x%21%29\"\r
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\n" ); document.write( "\n" ); document.write( "P(6) = \"%28e%5E%28-1.5%29%2A%281.5%29%5E6%29%2F%286%21%29\"\r
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\n" ); document.write( "\n" ); document.write( "P(6) = 0.00352998886172 which is approximate.\r
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\n" ); document.write( "\n" ); document.write( "Answer: Approximately 0.0035
\n" ); document.write( "This is about a 0.35% chance.
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