According to a survey, $10 \%$ of Americans are afraid to fly. Suppose 1,100 Americans are sampled.
b. What is the probability percentage that 165 or more Americans in the survey are afraid to fly? Round the percent to two decimal places.
c. What is the probability percentage that $8 \%$ or less of the Americans surveyed answered they were afraid to fly? Round the percent to two decimal places.
Answer
Final Answer: The probability that 165 or more Americans in the survey are afraid to fly is approximately \(\boxed{0.00001263 \%}\). The probability that 8\% or less of the Americans surveyed answered they were afraid to fly is approximately \(\boxed{1.34 \%}\).
Step 1 ：This problem is about finding the probability of a certain number of successes (people afraid to fly) in a given number of trials (the number of people surveyed). This is a binomial distribution problem.
Step 2 ：For part b, we need to find the probability that 165 or more Americans are afraid to fly. This is equivalent to finding the cumulative probability from 165 to 1100 (the total number of people surveyed).
Step 3 ：For part c, we need to find the probability that 8% or less of the Americans surveyed are afraid to fly. This is equivalent to finding the cumulative probability from 0 to 88 (8% of 1100).
Step 4 ：Let's denote the total number of people surveyed as \(n = 1100\), the probability of success (an American being afraid to fly) as \(p = 0.1\), and the number of successes as \(x\).
Step 5 ：For part b, we find that the probability is approximately \(1.262644458575009e-07\), or \(0.00001263\%\).
Step 6 ：For part c, we find that the probability is approximately \(0.013368830896570701\), or \(1.34\%\).
Step 7 ：Final Answer: The probability that 165 or more Americans in the survey are afraid to fly is approximately \(\boxed{0.00001263 \%}\). The probability that 8\% or less of the Americans surveyed answered they were afraid to fly is approximately \(\boxed{1.34 \%}\).
