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Busy Tellers - National Bank

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Busy Tellers. Prescott National Bank has six tellers available to serve customers. The number of tellers busy with customers at, say, 1:00 P.M. varies from daya to day and depends on chance, so it is a random variable, say, X. Past records indicate that the probability distribution of X is as shown in the following table.

x 0 1 2 3 4 5 6
P(X=x) 0.029 0.049 0.078 0.155 0.212 0.262 0.215

For example, the probability is 0.262 that exactly five of the tellers will be busy with customers at 1:00 P. M.; that is, about 26.2% of the time, exactly five tellers are busy with customers at 1:00 P. M. Use random-variables notation to represent each of the following events and then calculate the probabilities. At 1:00 P. M.,
(a) exactly four tellers are busy.
(b) At least two tellers are busy.
(c) Fewer than five tellers are busy.
(d) At least two but fewer than five tellers are busy.

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The expert analyzes busy tellers in the national bank. The probability distribution is given.

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