SOLUTION: A brand name has a 40​% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 5 randomly selected consumers. Complete part

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Question 1145746: A brand name has a 40​% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 5 randomly selected consumers. Complete parts​ (a) through​ (d) below.
a. What is the probability that exactly 4 of the selected consumers recognize the brand​ name?
The probability that exactly 4 of the 5 consumers recognize the brand name is
0.131.
​(Round to three decimal places as​ needed.)
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
p(4) = .4^4 * .6^1 * c(5,4) = .0768 = .077

this is a binomial distribution type problem where p(x) = p^x * q^(n-x) * c(n,x)

n is equal to 5
x ranges from 0 to 5.
c(n,x) = n! / (x! * (n-x)!)

the following excel spreadsheet shows all the probabilities from x = 0 to x = 5.
the sum of all the probabilities is equal to 1, as it should be.

$$$





Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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This is a binomial distribution type problem where p(x) = C(n,x)* p^x * q^(n-x)


    n is equal to 5               // number of trials
    x is equal to 4               // number of success trials
    p is the probability of success trial
    q = 1 - p
    C(n,x) = n! / (x! * (n-x)!)   // binomial coefficient


In your case  p(4) = C(5,4) * 0.4^4 * 0.6^1 = use Excel function BINOM.DIST(4, 5, 0.4, FALSE) = 0.0768.    ANSWER


On Excel function BINOM.DIST, see its description everywhere, for example

https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c


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