SOLUTION: A recent study found that 40% of all people over age of 62 wear hearing aids. If a random sample of 5 people over 62 is selected, find the probability of at least 4 wear hearing

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Question 1174020: A recent study found that 40% of all people over age of 62 wear hearing aids. If a random sample of 5 people over 62 is selected, find the probability of at least 4 wear hearing aids. (please round off into 3 decimal places).
Answer by ikleyn(52878) About Me  (Show Source):
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A recent study found that 40% of all people over age of 62 wear hearing aids. If a random sample of 5 people over 62 is selected,
find the probability of at least 4 wear hearing aids. (please round off into 3 decimal places).
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At least 4 means 4 or 5.


It is the binomial type probability distribution.


The number of trial n= 5; the probability of the success trial is  40% = 0.4,  and the number of success trial is  k = 4  and  k= 5. 


    P(4) = C%5B5%5D%5E4%2A0.4%5E4%2A%281-0.4%29%5E1 = 4%2A0.4%5E4%2A0.6 = 0.06144;


    P(5) = C%5B5%5D%5E5%2A0.4%5E5%2A%281-0.4%29%5E0 = 1%2A0.4%5E5     = 0.01024.


We want to get the sum  P = P(4) + P(5) = 0.06144 + 0.01024 = 0.07168.     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.