Question

A real estate agent has 19 properties that she shows. She feels that there is a 30 % chance of selling any one property during a

week. The chance of selling any one property is independent of selling another property. Compute the probability of selling at
least 5 properties in one week. Round your answer to four decimal places.

Answer 1

Answer: This is a binomial probability problem. Let X be the number of properties sold during a week, then X has a binomial distribution with parameters n=19 and p=0.3.

The probability of selling at least 5 properties is:

P(X ≥ 5) = 1 - P(X < 5)

To calculate P(X < 5), we can use the binomial cumulative distribution function or the normal approximation to the binomial distribution.

Using the binomial cumulative distribution function, we have:

P(X < 5) = Σ P(X = k) for k = 0 to 4

Using the formula for the binomial probability mass function, we get:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (0.7)^19 + 19(0.3)(0.7)^18 + 171(0.3)^2(0.7)^17 + 969(0.3)^3(0.7)^16 + 3876(0.3)^4(0.7)^15

Using a calculator or statistical software, we get:

P(X < 5) = 0.95044

Therefore, the probability of selling at least 5 properties in one week is:

P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.95044 = 0.0496 (rounded to four decimal places).

So the probability of selling at least 5 properties in one week is approximately 0.0496 or 4.96%.

Explanation: