# Thread: Complement Rewriting: Poisson, Binomial

1. ## Complement Rewriting: Poisson, Binomial

In terms of Poisson and Binomial distributions, what is the complement of:
* At least half
* More than

1. Customers returning items to a store arrive at the customer service desk according to a Poisson process with arrival rate of 18 per 30 minute interval. The probability that an arriving person is extremely upset is 50%. What is the chance that more than 100 extremely upset customers arrived between 7 and 8 pm?

2. Now suppose that exactly 30 customers arrived in the first half hour of operations. What is the probability that at least half of them are extremely upset?

I know I have to rewrite these in terms of complements, but I'm not quite sure how.

2. Originally Posted by MathGeek06
In terms of Poisson and Binomial distributions, what is the complement of:
* At least half
* More than

1. Customers returning items to a store arrive at the customer service desk according to a Poisson process with arrival rate of 18 per 30 minute interval. The probability that an arriving person is extremely upset is 50%. What is the chance that more than 100 extremely upset customers arrived between 7 and 8 pm?

2. Now suppose that exactly 30 customers arrived in the first half hour of operations. What is the probability that at least half of them are extremely upset?

I know I have to rewrite these in terms of complements, but I'm not quite sure how.
2. Let X be the random variable number of extremely upset customers in the group of 30.

X ~ Binomial( n = 30, p = 1/2).

You need to calculate $\displaystyle \Pr(X \geq 15) = 1 - \Pr(X leq 14)$.