Thread: 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.

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 .