A disease affects 9% of individuals in a population and a sample of 100 people is selected from the population. What is the probability of finding the disease in 15 people?
To calculate the probability of finding the disease in 15 people out of a sample of 100, we can use the binomial probability formula.
The binomial probability formula is given by:
P(x) = (nCx) * p^x * (1 - p)^(n - x)
Where:
P(x) is the probability of getting exactly x successes
n is the total number of trials
x is the number of successes
p is the probability of success in a single trial
In this case, the probability of having the disease in the population is given as 9%, or 0.09. The sample size is 100 people, and we want to find the probability of 15 people having the disease.
Plugging the values into the formula, we have:
P(15) = (100C15) * (0.09)^15 * (1 - 0.09)^(100 - 15)
Calculating this using a calculator or statistical software, we can find the value of P(15), which will give us the probability of finding the disease in 15 people out of the sample of 100.