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Answer:
The average number of phone calls in a 30 minute period is 3.
The probability to receive exactly 2 calls in that period is 0.224.
Step-by-step explanation:
If we are using the same Poisson distribution in the 2 hour period, then the average of phone orders in a reduced interval will be reduced according to that interval. Since 30 minutes is four times smaller than 2 hours, then the average number of phone orders per 30 minutes is 12 * 1/4 = 3. This can also be computed with a Rule of 3
120 minutes -------------> 12 orders
30 minutes ---------------> X orders
X = 30*12/120 = 3
Lets call Y the amount of phone orders received during a specific (random) 30 minute period. Since the average was 3, then Y has a Poisson distribution with parameter 3. The probability of Y being equal to 2 is
Thus, the probability to receive exactly 2 calls in a 30 minute period is 0.224.