A research team conducted a study showing that approximately 15% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)
(1) at least one tie is too tight
(2) more than two ties are too tight
(c) no tie is too tight

Question

A research team conducted a study showing that approximately 15% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)
(1) at least one tie is too tight
(2) more than two ties are too tight
(c) no tie is too tight

otherworldly · Answer

there are 20 people and 15% out of 100% have there ties on too tightly what do u think the answer is

otherworldly · Answer

which one is most likely wrong?

otherworldly · Answer

@grayj200

grayj200 · Answer

You have to answer each separately, it's not multiple choice those are separate questions. I know it binomial probability but I'm not sure how to plug the data into the formula.

agent0smith · Answer

Binomial probability. http://fsweb.bainbridge.edu/dbyrd/statistics/binomial_formula.gif p=0.15 q=0.85 n=20 (1) at least one tie is too tight $$\large P(X \ge 1) = 1- P(X = 0)$$Now use the binomial formula to find P(X=0) (2) more than two ties are too tight $$\large P(X \ge 2) = 1- P(X <2 )$$where$$\large P(X<2) = P(X=0)+P(X=1)$$so use the formula to find P(X=0) and P(X=1), then do math. (c) no tie is too tight (now why did it go 1, 2, c?) You want $\large P(X=0)$ and you already have that from your above calculations...

grayj200 · Answer

I appreciate the help, but that was counted wrong, you have to use the binomial probability formula, which I've been struggling with. I know the formula, it's just using in the correct way that trips me up. Also I meant to number the questions 1, 2 & 3, but forgot to change c, I was trying to make it look less like a multiple choice question

grayj200 · Answer

Thanks agent0smith

grayj200 · Answer

Could you work out one of the questions and show the steps? I don't want to mess any of them up. I feel so dumb when it comes to statistics. All math really.

agent0smith · Answer

Set it up like this$$\Large P(X=k) = \left(\begin{matrix}20 \ k\end{matrix}\right)0.15^k*0.85^{20-k}$$then go back and plug in the relevant values of k. (you only need to do it for k=0 and k=1)

$$\Large P(X=0) = \left(\begin{matrix}20 \ 0\end{matrix}\right)0.15^0*0.85^{20-0}$$I assume you can work out the combinations part of it

$$\Large P(X=1) = \left(\begin{matrix}20 \ 1\end{matrix}\right)0.15^1*0.85^{20-1}$$Work out both of those, then go back and use what I first gave.

grayj200 · Answer

Ok so, the 20 over one/zero is that a fraction or?

agent0smith · Answer

Not fractions. It's combinations. I assume you're familiar with combinations formula, if not, google is. Calculators have a button for it. 

*Correction for (2)

MORE than 2 means at least 3.
$$\large P(X \ge 3) = 1- P(X \le2 ) $$where$$\large P(X \le 2) = P(X=0)+P(X=1)+P(X=2)$$and $$\Large P(X=2) = \left(\begin{matrix}20 \ 2\end{matrix}\right)0.15^2*0.85^{20-2}$$

grayj200 · Answer

OH! Yes, I can use my calculator to do combinations.

grayj200 · Answer

I just wasn't sure usually I see them written as 20C2 or something among those lines, but thank you so much for your help.

agent0smith · Answer

Yeah, I usually write it as 20C2 as well.

Welcome.