Question

Eighty-five mall customers were randomly surveyed across the state to determine if the live entertainment provided had increased the amount of money they spent. Can the probability be found by using the binomial probability formula?

Answer 1

Yes (under certain conditions)

Explanation:

Binomial probability formula can be used if there are success and failure been discussed in the question.

The formula is given by

P(X=x) = \binom{n}{x}p^{x}q^{n-x}

where n= no. trials

p = success

q= failure

x= point at which we need to find the probability

Here, 85 customers are surveyed, then n= 85

we will take, p= live entertainment had increased the amount of money they spent (success)

q = live entertainment had not increased the amount of money they spent (failure)

x should be defined, then only we can use binomial probability formula

Example, x= 10 customers said that the money they spent increased if the live entertainment provided.

Answer 2

Yes

Explanation:

Binomial distribution is valid for trials which consist of only two outcomes, and each trial is independent of the other.

Here 85 mall customers were randomly surveyed. We have that each customers is independent of the other for the state o determine if the live entertainment provided had increased the amount of money they spent

Hence probability for each person to say yes can be taken as p and q =1-p for no reply.

There are only two outcomes.

Also n =85 is sufficiently large to have np or nq >5

Hence the probability can be found using binomial probability formula provided p = probability for success of a single trial is given.