SOLUTION: One quarter of all residents of Centerville are under 22 years old. If a random sample of twenty Centerville residents is selected, find the probability that the sample will contai

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Question 1186186: One quarter of all residents of Centerville are under 22 years old. If a random sample of twenty Centerville residents is selected, find the probability that the sample will contain exactly four people who are under 22 years old. (The total population of Centerville is about 40,000.)
Write your answer as a decimal, rounded to three significant figures.
Answer by ikleyn(52799) About Me  (Show Source):
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One quarter of all residents of Centerville are under 22 years old.
If a random sample of twenty Centerville residents is selected, find the probability
that the sample will contain exactly four people who are under 22 years old.
(The total population of Centerville is about 40,000.)
Write your answer as a decimal, rounded to three significant figures.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

This is a binomial distribution problem with  n = 20 trials  and 
the probability of success for each individual trial  p = 1/4 = 0.25.


The problem asks to find the probability of getting k= 4 successful trials among n = 20 total trials.


Use the standard formula for such probability

    P = C%5B20%5D%5E4%2Ap%5E4%2A%281-p%29%5E%2820-4%29 = %28%2820%2A19%2A18%2A17%29%2F%281%2A2%2A3%2A4%29%29%2A0.25%5E4%2A0.75%5E16 = 0.190  (rounded as requested).     ANSWER

Solved.