The average number of houses sold by a company is 2 houses per day what is the probability that exactly 3 houses will be sold in one week
Need to know some measure of variability.
To find the probability of exactly 3 houses being sold in one week, we need to consider the number of ways 3 houses can be sold in a week out of all possible outcomes.
To begin, let's calculate the number of ways to sell 3 houses in a week. Since the average number of houses sold per day is 2, we can assume the number of houses sold in a day follows a Poisson distribution. The formula to find the probability mass function (PMF) of a Poisson distribution is:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where:
P(x; λ) is the probability of x events occurring in a given time frame, λ is the average number of events in that same time frame, e is the base of the natural logarithm (approximately 2.71828), and x! represents the factorial of x.
In our case, x = 3, as we want to find the probability of selling exactly 3 houses in a week. Additionally, the average number of houses sold per day is 2, so λ = 2.
Now we can substitute these values into the formula:
P(3; 2) = (e^(-2) * 2^3) / 3!
Applying the values and performing the calculations:
P(3; 2) = (e^(-2) * 8) / 6
P(3; 2) ≈ 0.180
Therefore, the probability of exactly 3 houses being sold in one week is approximately 0.180, or 18.0%.