According to CTIA, 41% of all U. S. households are wireless-only households (no landline). In a random sample of 20mhouseholds, what is the probability that.1. Exactly 5 are wireless-only? 2. Fewer than 3 are wireless-only?3. At least 3 are wireless-only?4. The number of households that are wireless-only is between 5 and 7, inclusive?

1)

2)

And we can find the individual probabilities and we got:

And adding we got:

3)

And using the complment rule we have this:

And using the result form the previous result we got:

4)

And we can find the individual probabilites and we got:

And adding we got:

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

Part 1

We want this probability:

We can use th probability mass function and we got:

Part 2

We want this probability:

And we can find the individual probabilities and we got:

And adding we got:

Part 3

For this case we want this probability:

And using the complment rule we have this:

And using the result form the previous result we got:

Part 4

For this case we want this probability:

And we can find the individual probabilites and we got:

And adding we got:

the correct answer is 828.07