I would like to be verified in this problem. Thanks in advance.
A call-center receives, on average, 15 calls per hour.
1. Find the probability that at least 8 calls are received in a 2.5hrs
So if on average are received 15 calls per hour, in 2.5hr are received 37.5 calls.
$$P(x\geq8)=1-P(x<8)$$ $$P(x\geq8)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)+P(x=7)]$$ $$P(x\geq8)=1-0.018$$ $$P(x\geq8)=0.982$$
2. If a call is received at 1:15 pm, find the probability that the next call is receive by 1:30pm.
So if on average are received 15 calls per hour, in 15min are received 3.75 calls.
$$P(x\geq1)=1-P(x=0)=1-0.024=0.976$$