transportation officials tell us that 80% of drivers wear seat belt while driving. Find the probability that more then 567 drivers in a sample of 700 drivers wear seat belts
To find the probability that more than 567 drivers in a sample of 700 drivers wear seat belts, we need to use the binomial probability formula. The binomial probability formula is:
P(X > k) = 1 - P(X ≤ k)
Where P(X > k) is the probability of getting more than k successes, P(X ≤ k) is the probability of getting k or fewer successes, and X is a binomial random variable.
In this case, we are given that 80% of drivers wear seat belts. So, the probability of a driver wearing a seat belt is 0.8. Let's denote this probability as p.
Now, let's calculate the probability of getting 567 or fewer drivers wearing seat belts.
P(X ≤ 567) = C(700, 0) * p^0 * (1-p)^(700-0) + C(700, 1) * p^1 * (1-p)^(700-1) + ... + C(700, 567) * p^567 * (1-p)^(700-567)
To calculate this probability, we would need to compute the cumulative sum of the above terms. However, this would involve a very lengthy calculation. Instead, we can use a statistical software or a binomial calculator to find the exact probability.
Once we have the probability of getting 567 or fewer drivers wearing seat belts, we can find the probability of more than 567 drivers wearing seat belts using:
P(X > 567) = 1 - P(X ≤ 567)
By substituting the calculated value of P(X ≤ 567) into the equation, we can find the probability of more than 567 drivers in a sample of 700 drivers wearing seat belts.