In a study, 37 % 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 13 adults randomly selected from this area, only 3 reported that their health was excellent. find the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health. round to three decimal places.

0.230

Step-by-step explanation:

Probability of an adult being in excellent health = p = 37% = 0.37

This satisfies all the 4 conditions that are needed for a Binomial Experiment. Hence, we can solve the given question using Binomial Probability.

p = 0.37

q = 1 - p = 1 - 0.37 = 0.63

n = 13

We need to find the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health i.e. P( x ≤ 3 )

P( x ≤ 3 ) = P(0) + P(1) + P(2) + P(3)

The formula of Binomial probability is:

So,

Thus,

P( x ≤ 3 ) = P(0) + P(1) + P(2) + P(3) = 0.0025 + 0.0188 + 0.0663 + 0.1427

P( x ≤ 3 ) = 0.2303

Therefore, the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health is 0.230

c

step-by-step explanation: