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dexar [7]
3 years ago
15

In a​ study, 36​% of adults questioned reported that their health was excellent. A researcher wishes to study the health of peop

le living close to a nuclear power plant. Among 1111 adults randomly selected from this​ area, only 3 reported that their health was excellent. Find the probability that when 1111 adults are randomly​ selected, 3 or fewer are in excellent health. Round to three decimal places.
Mathematics
1 answer:
steposvetlana [31]3 years ago
5 0

Answer:

0.3907

Step-by-step explanation:

We are given that 36​% of adults questioned reported that their health was excellent.

Probability of good health = 0.36

Among 11 adults randomly selected from this​ area, only 3 reported that their health was excellent.

Now we are supposed to find the probability that when 11 adults are randomly​ selected, 3 or fewer are in excellent health.

i.e. P(x\leq 3)=P(x=1)+{P(x=2)+P(x=3)

Formula :P(x=r)=^nC_r p^r q ^ {n-r}

p is the probability of success i.e. p = 0.36

q = probability of failure = 1- 0.36 = 0.64

n = 11

So, P(x\leq 3)=P(x=1)+{P(x=2)+P(x=3)

P(x\leq 3)=^{11}C_1 (0.36)^1 (0.64)^{11-1}+^{11}C_2 (0.36)^2 (0.64)^{11-2}+^{11}C_3 (0.36)^3 (0.64)^{11-3}

P(x\leq 3)=\frac{11!}{1!(11-1)!} (0.36)^1 (0.64)^{11-1}+\frac{11!}{2!(11-2)!}  (0.36)^2 (0.64)^{11-2}+\frac{11!}{3!(11-3)!} (0.36)^3 (0.64)^{11-3}

P(x\leq 3)=0.390748

Hence  the probability that when 11 adults are randomly​ selected, 3 or fewer are in excellent health is 0.3907

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