Need help on simple binomial problem

[kiurys]

Hello everyone,

Just have a quick question on a binomial problem.

The problem is as follows:

A teacher is giving a 15 question true-false quiz. He wants to design the quiz such that a person that guesses on all the answers have less than a 0.10 probability of passing. What should the teacher put as the passing number of questions to achieve this?

I have no idea how to do this.

 

[statdad]

Suppose you call the number of correct responses needed to pass $a$. If $X$ is the number of correc responses from 15 guesses, what must be the relation between $X$ and $a$ in order to pass?

 

[kiurys]

I have my test in half an hour and that was the only question I didnt know how to do from the review.

So let A be the number needed to pass, then:

P(A) = 15_C_A * (0.5)^A * (0.5)^(15-A) = 15_C_A * (0.5)^15 = 0.000030518 * 15_C_A = 0.000030518 * [(15!)/(A!)(15-A)!]

and since I want P(A) < 0.10 then:

0.000030518 * [(15!)/(A!)(15-A)!] < 0.10

and solve for A? (no idea how to solve involving a factorial like that) Is this the way to go about this? A quick response will be appreciated :)