Question

A brand name has a 60​% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 4
randomly selected consumers.

What is the probability that exactly
3 of the selected consumers recognize the brand​ name?

Answer 1

You can use the binomial distribution to solve this.

Answer 2

\[P(x)=\frac{ n! }{ (n-x)!x! }*p ^{x}*q ^{n-x}\]
That's the formula I have in my notes but I also have a chart that I don't understand how I got the numbers.

Answer 3

That is the correct formula. Putting in the numbers we get:
\[\large \frac{4!}{(4-3)!3!}\times0.6^{3}\times(1-0.6)^{(4-3)}=?\]

Answer 4

.3456?

Answer 5

I think what I'm really confused by is the binomial probabilities table they want me to make. They provided an example and I'm not comprehending how they got their numbers.

Answer 6

If the table relates to this question, I assume that the table would show the probabilities of exactly 0, 1, 2, 3 and 4 of the selected consumers recognize the brand​ name.

Answer 7

Your calculation of P(exactly 3 consumers) is correct.

Answer 8

Hm. Okay. so P(3) on the chart would be the same as my answer above? Or am I still confused?

Answer 9

Without having seen the chart, it appears that you are on the right track.

Answer 10

Thanks, Kropot72! I ended up getting it correct.

Answer 11

Good work! You're welcome :)