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December 31st, 2016, 06:47 AM   #1
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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.
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December 31st, 2016, 01:49 PM   #2
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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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