232k views
0 votes
As of 2021, 35% of all vehicles on the road were white. Suppose a random sample is taken of 300 cars. What is the probability that at most 30% are white? Must show all work.

User DongYao
by
8.2k points

1 Answer

2 votes

Final answer:

To find the probability that at most 30% of the 300 cars in a random sample are white, we can use the binomial distribution and calculate the probability using the binomial probability formula.

Step-by-step explanation:

To find the probability that at most 30% of the 300 cars in a random sample are white, we need to use the binomial distribution. Let's define a success as a car being white and a failure as a car being any color other than white. The probability of success is 35% (0.35) and the probability of failure is 65% (1 - 0.35). We can use the binomial probability formula to calculate the probability:

P(X ≤ k) = ∑ (k = 0 to k)

Where:

  • P(X ≤ k) is the probability that at most k successes occur
  • n is the number of trials (300)
  • p is the probability of success (0.35)
  • k is the number of successes

Let's calculate the probability:

  1. P(X ≤ 30) = ∑ (k = 0 to 30) [300Ck * (0.35)^k * (1 - 0.35)^(300 - k)]
  2. Using a binomial distribution calculator or software, we find that P(X ≤ 30) ≈ 0.6538

Therefore, the probability that at most 30% of the cars in the random sample are white is approximately 0.6538 or 65.38%.

User Sohil Pandya
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories