People's arrivals at a register occur at a constant rate of 7 per hour. It  will take about 10 minutes to service each person and that an unlimited number of servers are available, so no one has to wait for service. For a given hour, find the probability exactly 7 customers arrive.  For a given hour, find the probability fewer than 3 customers arrive. For a given hour, find the probability at least 2 customers arrive. Find the mean and variance of the total service time for 1 hour. Find the probability that exactly 5 customers arrive between 2 and 4 p.m. Find the probability that exactly 5 customers between 1 and 2 p.m., and between 3 and 4 p.m.

MATLAB: An Introduction with Applications
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People's arrivals at a register occur at a constant rate of 7 per hour. It  will take about 10 minutes to service each person and that an unlimited number of servers are available, so no one has to wait for service. For a given hour, find the probability exactly 7 customers arrive.  For a given hour, find the probability fewer than 3 customers arrive. For a given hour, find the probability at least 2 customers arrive. Find the mean and variance of the total service time for 1 hour. Find the probability that exactly 5 customers arrive between 2 and 4 p.m. Find the probability that exactly 5 customers between 1 and 2 p.m., and between 3 and 4 p.m.

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Given that rate of arrival left parenthesis lambda right parenthesis = 7 per hour and we can assume that arrival rate follows Poisson distribution whose pdf is given as:

P(X=x) = fraction numerator e to the power of negative lambda end exponent lambda to the power of x over denominator x factorial end fraction comma space x equals 0 comma 1 comma 2 comma....

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