SOLUTION: In a study, 40% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 10 adu

Question 1067796: In a study, 40% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 10 adults randomly selected from this area, only 3 reported that their health was excellent.
Find the probability that when 10 adults are randomly selected, 3 or fewer are in excellent health.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We the binomial probability formula
:
Probability(P) (k events out of n trials) = nCk * p^k * (1-p)^(n-k), where p=0.40, n=10 and nCk is the number of combinations of n things taken k at a time
:
P ( k < or = 3 ) = P ( k = 3 ) + P ( k = 2 ) + P ( k = 1 ) + P ( k = 0 )
:
P ( k = 3 ) = 10C3 * (0.40)^3 * (0.60)^(10-3) = 0.2149
:
P ( k = 2 ) = 10C2 * (0.40)^2 * (0.60)^(10-2) = 0.1209
:
P ( k = 1 ) = 10C1 * (0.40)^1 * (0.60)^(10-1) = 0.0403
:
P ( k = 0 ) = 10C0 * (0.40)^0 * (0.60)^(10-0) = 0.0060
:
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P ( k < or = 3 ) = 0.2149 + 0.1209 + 0.0403 + 0.0060 = 0.3821 is approximately 0.38
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