SOLUTION: 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, w

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Question 1176264: 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.
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
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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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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%5B12%5D%5E3%2A0.5%5E3%2A%281-0.5%29%5E%2812-3%29 = %28%2812%2A11%2A10%29%2F%281%2A2%2A3%29%29%2A0.5%5E3%2A0.5%5E9 = 220%2A0.5%5E12 = 0.0537 = 5.37% (rounded).     ANSWER

Solved.

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To see many other similar solved problems, look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.