An internet service provider uses 50 modems to serve the needs of 1000 customers. It is estimated that at a given time. each customer will need a connection with probability 0.01, independent of the other customers.
What is the probability mass function of the number of modems in use at the given time?

The probability mass function of the number of modems in use at the given time is:

Step-by-step explanation:

Let the random variable X = number of modems in use.

The internet provider uses 50 modems.

The number of customers served by the internet user is, n = 1000.

The probability that a customer will require an internet connection is, p = 0.01.

It is provided that the customers are independent of each other.

The random variable X satisfies all the properties of a Binomial distribution with parameters n = 1000 and p = 0.01.

The probability mass function of a Binomial distribution is:

Then the probability mass function of the number of modems in use at the given time is:

11 feet 6 inches and 8 feet 6 inches

step-by-step explanation: