document.write( "Question 618563: I have 1000 completely independent events E1, E2, E3... E1000 that each have a 5% chance of occurring any given day.
\n" ); document.write( "1. How can I predict with say 90% confidence how many events occur on any given day?
\n" ); document.write( "2. What is the probability that at least 100 items occur on a given day?\r
\n" ); document.write( "\n" ); document.write( "Could you please explain the solution too? \r
\n" ); document.write( "\n" ); document.write( "Thanks! \n" ); document.write( "
Algebra.Com's Answer #388989 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
I have 1000 completely independent events E1, E2, E3... E1000 that each have a 5% chance of occurring any given day.
\n" ); document.write( "Binomial Problem with n = 1000 and p(occur) = 0.05 ; P(not occur) = 0.95
\n" ); document.write( "------------------------------------------------
\n" ); document.write( "1. How can I predict with say 90% confidence how many events occur on any given day?
\n" ); document.write( "mean = np = 1000*0.05 = 50
\n" ); document.write( "std = sqrt(npq) = sqrt(50*0.95) = 6.89
\n" ); document.write( "---
\n" ); document.write( "Lower limit: 50-1.645*6.89 = 38.67
\n" ); document.write( "Upper limit: 50+1.645*6.89 = 61.33
\n" ); document.write( "===============================================\r
\n" ); document.write( "\n" ); document.write( "2. What is the probability that at least 100 items occur on a given day?
\n" ); document.write( "P(100<= x <=1000) = 1 - P(0<= x <=99) = 1 - binomcdf(1000,0.05,99)
\n" ); document.write( "= 8.41x10^(-11)
\n" ); document.write( "===================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "=================== \n" ); document.write( "
\n" );