Question

It was reported that 23% of U.S. adult cellphone owners called a friend for advice about a purchase while in a store. If a sample of 15 U.S adult cellphone owners is selected, what is the probability that 7 called a friend for advice about a purchase while in a store

Answer 1

`P(X=7)`

And using the probability mass function we got:

`P(X=7)=(15C7)(0.23)^7 (1-0.23)^(15-7)=0.0271`

Explanation:

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

`X \sim Binom(n=15, p=0.23)`

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

`P(X)=(nCx)(p)^x (1-p)^(n-x)`

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

`nCx=(n!)/((n-x)! x!)`

And we want to find the following probability:

`P(X=7)`

And using the probability mass function we got:

`P(X=7)=(15C7)(0.23)^7 (1-0.23)^(15-7)=0.0271`