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

Answer:

$P(X=7)$

And using the probability mass function we got:

$P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271$  

Step-by-step 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:  

$nCx=\frac{n!}{(n-x)! x!}$  

And we want to find the following probability:

$P(X=7)$

And using the probability mass function we got:

$P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271$