In a study, 4040% 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 1212 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 1212 adults are randomly selected, 3 or fewer are in excellent health. Round to three decimal places.

0.225 is the probability that 3 or fewer than 3 adults are in excellent health.

Step-by-step explanation:

We are given the following information:

We treat adult with excellent health as a success.

P(Adult with excellent health) = 40% = 0.4

Then the number of adults follows a binomial distribution, where

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 12

We have to evaluate:

0.225 is the probability that 3 or fewer than 3 adults are in excellent health.

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.