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Busy Tellers - National Bank

I got confussed with this one. So if you can help me out. Thank You

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.

Solution Preview

a) P(4) = .212 (From the table)
<br>b) P(>=2) = 1 - P(0)+ P(1)
<br> ...

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