Question

A drug test is accurate 97% of the time. if the test is given to 1800 people who have not taken drugs, what is the probability that at least 55 will test positive?

Answer 1

To find the probability of at least 55 people testing positive out of 1800, we can use the binomial probability formula. Calculate P(X < 55) using the binomial probability formula and subtract it from 1 to find P(X >= 55). Use a calculator or statistical software to perform the calculations.

Step-by-step explanation:

To find the probability of at least 55 people testing positive out of 1800, we can use the binomial probability formula:

P(X >= 55) = 1 - P(X < 55)

where X follows a binomial distribution with n = 1800 and p = 0.97. Calculate P(X < 55) using the binomial probability formula and then subtract it from 1 to find P(X >= 55).

Using the binomial probability formula:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Let's calculate:

P(X < 55) = P(X=0) + P(X=1) + ... + P(X=54)

Since this calculation can be tedious, it's recommended to use a calculator or statistical software that can calculate cumulative binomial probabilities.