The number of calls coming to a call center follows a Poisson distribution. On t

Question

The number of calls coming to a call center follows a Poisson distribution. On the average 90 calls arrive every hour on Mondays between 10:00 and 11:00 a.m. The probability that exactly four calls will arrive in a three minute period is:

(a) 0.2152 (b) 0.2240 (c) 0.2205 (d) 0.1899 (e) 0.2232

The number of passengers arriving at a checkout counter of an international airport follows a Poisson distribution. On the average 6 customers arrive every 5minute period. The probability that over any 5minute interval, exactly 5 passengers will arrive at the checkout counter is:

(a) 0.0811 (b) 0.0925 (c) 0.0220 (d) 0.1954 (e) 0.1606

A call center receives 48 calls on the average every hour on a busy Saturday morning between 10:00 and 11:00 a.m. The call center manager is interested in calculating the probability of receiving 8 calls in 15 minutes interval. This probability is:

(a) 0.5221 (b) 0.0848 (c) 0.0655 (d) 0.0295 (e) 0.0323

The number of passengers arriving at a checkout counter of an international airport follows a Poisson distribution. On the average 4 customers arrive every 5minute period. The probability that over any 10minute interval, at most 5 passengers will arrive at the checkout counter is:

(a) 0.1221 (b) 0.1250 (c) 0.2215 (d) 0.1912 (e) 0.8088

Explanation / Answer

a)

The number of calls coming to a call center follows a Poisson distribution. On the average 90 calls arrive every hour on Mondays between 10:00 and 11:00 a.m. The probability that exactly four calls will arrive in a three minute period is:

There are 90 calls/hr, so there are 90*(3min/60min) = 4.5 calls per 3 min.

Note that the probability of x successes is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    4.5      
          
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.1898076 = 0.1899 [ANSWER, D]

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