The average number of houses sold by a company is 2 houses per day what is probability that's exactly 3 houses will be sold in one week
To calculate the probability of exactly 3 houses being sold in one week, we need to use the concept of a Poisson distribution. The Poisson distribution is often used to model the probability of a given number of events occurring within a fixed interval of time, given the average rate at which those events occur.
In this case, the average number of houses sold by the company is 2 houses per day. We want to find the probability of exactly 3 houses being sold in one week, which consists of 7 days.
To use the Poisson distribution formula, which is:
P(x; λ) = (e^(-λ) * λ^x) / x!
where P(x; λ) is the probability of x events occurring given an average rate of λ.
First, we need to calculate the average rate of houses sold in one week. Since there are 7 days in a week, the average rate for one week is:
λ = average rate per day * number of days = 2 houses/day * 7 days = 14 houses/week.
Now, we can substitute the values into the Poisson distribution formula to find the probability of exactly 3 houses being sold in one week:
P(3; 14) = (e^(-14) * 14^3) / 3!
Using a calculator, we can evaluate this formula to find the answer.
P(3; 14) ≈ 0.041
Therefore, the probability that exactly 3 houses will be sold in one week is approximately 0.041, or 4.1%.