A restaurant gets an average of 12 phone orders in a 2 hour time period. In order to find the probability that the restaurant will get exactly 2 phone orders in a 30 minute period using the Poisson distribution, what is the average number of phone orders per 30 minutes?

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.

x = 12

y = 15

step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18