Question

a real estate agent has 20 properties that she shows. she feels that there is a 40% 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 less than 5 properties in one week. round your answer to four decimal places.

Explanation:

Identify the distribution parameters

Using the Binomial Distribution knowledge point

$$
LATEXBLOCK0
$$

Define the target probability

Using the Binomial Distribution knowledge point

$$ P(X < 5) = P(X \le 4) = \sum_{k=0}^{4} \binom{20}{k} (0.40)^k (0.60)^{20-k} $$

Calculate individual term probabilities

Using the Binomial Distribution knowledge point

$$
LATEXBLOCK1
$$

Sum the probabilities and round

Using the Binomial Distribution knowledge point

$$
LATEXBLOCK2
$$

Answer:

A real estate agent has 20 properties that she shows. She feels that there is a 40% 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 less than 5 properties in one week. Round your answer to four decimal places. <blank>0.0510</blank>