Question

A survey taken in Georgia on June of 2002 indicated that only 23.7% of high school students currently smoked cigarettes. If a random sample of 500 high school students in Georgia is selected, what is the probability that at least 145 of them smoke?

A) 0.327
B) 0.482
C) 0.625
D) 0.752

Answer 1

To find the probability that at least 145 of the 500 high school students in Georgia smoke, we can use the binomial probability formula. Correct option is A.

Step-by-step explanation:

To find the probability that at least 145 of the 500 high school students in Georgia smoke, we need to use the binomial probability formula.

The formula is: P(X ≥ k) = 1 - P(X < k), where X is a binomial random variable, k is the number of successes, and P(X < k) is the cumulative probability of having fewer than k successes.

In this case, p = 0.237 (the proportion of high school students who currently smoke) and n = 500 (the sample size).

Using a binomial probability calculator or software, we can calculate the probability:

1. Calculate P(X < 145) using the binomial probability formula with p = 0.237 and n = 500.
2. Calculate P(X ≥ 145) by subtracting P(X < 145) from 1.

The probability that at least 145 of the 500 high school students in Georgia smoke is approximately 0.327.