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Answer:
The probability that when 11 adults are randomly selected, 3 or fewer are in excellent health is 0.6483.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of adults questioned reported that their health was excellent.
A random sample of <em>n</em> = 11 adults are selected randomly selected from an area a nuclear power plant.
Of these 11 adults <em>X</em> = 3 reported that their health was excellent.
The proportion of adults who reported that their health was excellent is:
An adult's health condition is not affected by others, i.e. they are independent.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 11 and <em>p</em> = .
The probability mass function of <em>X</em> is:
Compute the probability that when 11 adults are randomly selected, 3 or fewer are in excellent health as follows:
P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
Thus, the probability that when 11 adults are randomly selected, 3 or fewer are in excellent health is 0.6483.