Question 1176264
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A researcher wishes to conduct a study of the color preferences of new car buyers. 
Suppose that 50% of this population prefers the color blue. 
If 12 buyers are randomly selected, what is the probability that exactly a fourth of the buyers 
would prefer blue? Round your answer to four decimal places.
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<pre>
It is the binomial type probability distribution.


"a fourth of the buyers" in this problem means  1/4  of 12, i.e. 3 buyers of 12.


The number of trial n= 12; the probability of the success trial is  0.5,  and the number of success trial k = 3. 


P = {{{C[12]^3*0.5^3*(1-0.5)^(12-3)}}} = {{{((12*11*10)/(1*2*3))*0.5^3*0.5^9}}} = {{{220*0.5^12}}} = 0.0537 = 5.37% (rounded).     <U>ANSWER</U>
</pre>

Solved.


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To see many other similar solved problems, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> 

in this site.