Jim is a real estate agent who sells large commercial buildings. Because his com

Question

Jim is a real estate agent who sells large commercial buildings. Because his commission is so large on a single sale, he does not need to sell many buildings to make a good living. History shows that Jim has a record of selling an average of 8.6 large commercial buildings every 264 days.

(b) In a 69-day period, what is the probability that Jim will make no sales? one sale? two or more sales? (Use 2 decimal places for . Use 4 decimal places for your answers.)

(c) In a 107-day period, what is the probability that Jim will make no sales? two sales? three or more sales? (Use 2 decimal places for . Use 4 decimal places for your answers.)

Explanation / Answer

(B)
8.6 sales in 264 days
hence, in 69 days number of sales would be 8.6*69/264 = 2.2477

Here lambda = 2.25
P(X=0) = lambda^0 * e^(-lambda)/0! = 0.1054

P(X=2) = lambda^2 * e^(-lambda)/2! = 0.2668

P(X=1) =  lambda^1 * e^(-lambda)/1! = 0.2372

P(X<2) = P(X=0) + P(X=1) = 0.1054 + 0.2372 = 0.3426

P(X>=2) = 1 - P(X<2) = 1 - 0.3426 = 0.6574

(C)
8.6 sales in 264 days
hence, in 107 days number of sales would be 8.6*107/264 = 3.4856

Here lambda = 3.49
P(X=0) = lambda^0 * e^(-lambda)/0! = 0.0306

P(X=2) = lambda^2 * e^(-lambda)/2! = 0.1861

P(X=1) =  lambda^1 * e^(-lambda)/1! = 0.1068

P(X<3) = P(X=0) + P(X=1) + P(X=2) = 0.0306 + 0.1068 + 0.1861 = 0.3235

P(X>=3) = 1 - P(X<3) = 1 - 0.3235 = 0.6765

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.