Final answer:
To find the probability of finding a sample of adults with a company pension, you can use the binomial distribution formula and calculate the probabilities for the given range of successes. Using the cumulative distribution function, the probability of finding a sample with a pension above 30 adults but no more than 45 adults is 0.04899.
Step-by-step explanation:
To find the probability of finding a sample of adults with a pension, we can use the binomial distribution. The formula for finding the probability of a range of successes in a binomial distribution is:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k),
where n is the sample size, k is the number of successes, C(n, k) is the number of combinations of n items taken k at a time, and p is the probability of success for each individual. In this case, n = 100, k ranges from 30 to 45, and p = 0.4. To find the probability of the given range, we need to sum the probabilities for each individual k value using the formula above. By using cumulative distribution function (cdf), we can calculate this probability.
Using a calculator or statistical software, we find that the probability of finding a sample with a pension above 30 adults but no more than 45 adults is 0.04899.