Answer
a. $0.5543$
b. $0.8488$
c. $0.4457$
Work Step by Step
Let $\lambda=6$ use Poisson formula or table:
a. At least 6 calls
We first calculate less than 6 calls, x=0,1,2,3,4,5
P(0,6)+P(1,6)+P(2,6)+P(3,6)+P(4,6)+P(5,6)=0.0025+0.0149+0.0446+0.0892+0.1339+0.1606=0.4457
For at least 6 calls: $P(x\geq6)=1-0.4457=0.5543$
b. 4 or more calls
We first find less than 4 calls, x=0,1,2,3
P(0,6)+P(1,6)+P(2,6)+P(3,6)=0.0025+0.0149+0.0446+0.0892=0.1512
For 4 or more calls $P(x\geq4)=1-0.1512=0.8488$
c. At most 5 calls, x=0,1,2,3,4,5
As in (a) $P(x\leq5)=0.4457$
