In a study,38% 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.
A)0.4336
B)0.3093
C)0.2017
D)0.5664
E)0.2319

Question

Quizplus · Accepted Answer

The probability of selecting an adult in excellent health is 0.38. The probability of selecting an adult not in excellent health is 1 - 0.38 = 0.62. The probability of selecting 3 or fewer adults in excellent health out of 10 is given by the binomial distribution:P(X ≤ 3) = Σ P(X = k) for k = 0, 1, 2, 3= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)= (0.62)^10 + 10(0.62)^9(0.38) + 45(0.62)^8(0.38)^2 + 120(0.62)^7(0.38)^3= 0.4336Therefore, the probability that when 10 adults are randomly selected, 3 or fewer are in excellent health is 0.4336.

In a Study,38% of Adults Questioned Reported That Their Health