Problem

According to a survey, $10 \%$ of Americans are afraid to fly. Suppose 1,100 Americans are sampled.
a. What is the probability percentage that 121 or moife Americans in the survey are afraid to fly? Round the percent to two decimal places. 14.59

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The probability percentage that 121 or more Americans in the survey are afraid to fly is \(\boxed{14.59\%}\).

Steps

Step 1 :This problem is about binomial distribution. We are given the probability of success (p), the number of trials (n), and we are asked to find the probability of having at least a certain number of successes (k).

Step 2 :The binomial distribution formula is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(C(n, k)\) is the combination of n items taken k at a time, \(p\) is the probability of success, and \((1-p)\) is the probability of failure.

Step 3 :However, we are asked to find the probability of having at least 121 successes, so we need to sum the probabilities from 121 to 1100.

Step 4 :Given that \(p = 0.1\), \(n = 1100\), and \(k = 121\), we calculate the probability and find it to be approximately 0.1459 or 14.59%.

Step 5 :Final Answer: The probability percentage that 121 or more Americans in the survey are afraid to fly is \(\boxed{14.59\%}\).

link_gpt