Question

A survey corps is collecting data on resource usage in an isolated village. The survey was specifically looking at the rate of infection from a shared water source for the villagers. Data showed that each villager, on average, had a 45% chance of infection each month they continued to drink locally sourced water. In a study sample of 100 villagers, what is the probability that between 42 and 68 villagers get sick in the next month?

Answer 1

the probability that between 42 and 68 villagers get sick in the next month is approximately 0.999998 or 99.9998%.

Explanation:

This problem can be solved using the binomial distribution. Let X be the number of villagers who get sick in a sample of 100. Then, X follows a binomial distribution with n=100 and p=0.45.

We want to find the probability that between 42 and 68 villagers get sick in the next month. We can use the cumulative probability function of the binomial distribution to calculate this probability:

P(42 <= X <= 68) = P(X <= 68) - P(X < 42)

Using a calculator or software, we can find:

P(X <= 68) = 0.999998

P(X < 42) = 1.22513e-12

Therefore,

P(42 <= X <= 68) = 0.999998 - 1.22513e-12

= 0.999998

So the probability that between 42 and 68 villagers get sick in the next month is approximately 0.999998 or 99.9998%.