SOLUTION: I have 1000 completely independent events E1, E2, E3... E1000 that each have a 5% chance of occurring any given day. 1. How can I predict with say 90% confidence how many events

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