You can use the binomial probability distribution

Solved Step by Step With Explanation- Probability of Supporting Gun Laws

Questions

Answer

To find the probability that at most 5 people out of a random sample of 10 support stricter gun laws when 72% of the population supports stricter gun laws, you can use the binomial probability distribution. The binomial distribution models the probability of success (supporting stricter gun laws) or failure (not supporting stricter gun laws) in a fixed number of independent trials (the sample size).

Now, you can calculate each of these probabilities using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

(n choose k) represents the number of ways to choose k successes out of n trials and is calculated as n! / (k! * (n - k)!.

Let's calculate each term:

P(X = 4) = (10 choose 4) * (0.72^4) * (0.28^6) ≈ 0.000782405285

P(X = 5) = (10 choose 5) * (0.72^5) * (0.28^5) ≈ 0.003158280800