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December 31st, 2016, 05:47 AM  #1 
Newbie Joined: Dec 2016 From: Pakistan Posts: 3 Thanks: 0  Two questions related to normal distribution
A telephone exchange receives, on average, 5 calls per minute. Find the probability that in a 20 minute period no more than 102 calls are received Exactly 90 calls are received and A radioactive element disintegrates such that it follows a Poisson distribution. If the mean number of particles emitted is recorded in a 1 second interval as 69, evaluate the probability of: Less than 60 particles are emitted in 1 second. Between 65 and 75 particles inclusive are emitted in 1 second. 
December 31st, 2016, 12:49 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,754 Thanks: 695 
First question: Unless you assume a Poisson distribution, there is not enough information. To use a normal approximation, you need a variance. To get a probability for exactly 90, use the exact formula (assuming Poisson). Second question: For a Poisson distribution the variance equals the mean. Look up table of normal distribution to get the probabilities for the particular mean and variance. 

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