Question

A real estate agent has 1717 properties that she shows. She feels that there is a 60`% 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 no more than 55 properties in one week. Round your answer to four decimal places.

Answer 1

`P(x \le 5) = 0.0110`

Explanation:

Given

`n = 17` -- number of properties

`p = 60\%` --- probability of selling a property

Required

`P(x \le 5)`

The question is an illustration of binomial probability, and it is calculated using:

`P(x ) = ^nC_x * p^x * (1 - p)^(n-x)`

So, we have:

`P(x \le 5) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3) +P(x = 4) +P(x = 5)`

`P(x=0 ) = ^(17)C_0 * (60\%)^0 * (1 - 60\%)^(17-0) = 1.71798692*10^(-7)`

`P(x=1 ) = ^(17)C_1 * (60\%)^1 * (1 - 60\%)^(17-1) = 0.00000438086`

`P(x=2 ) = ^(17)C_2 * (60\%)^2 * (1 - 60\%)^(17-1) = 0.00005257039`

`P(x=3 ) = ^(17)C_3 * (60\%)^3 * (1 - 60\%)^(17-3) = 0.00039427799`

`P(x=4 ) = ^(17)C_4 * (60\%)^4 * (1 - 60\%)^(17-4) = 0.00206995948`

`P(x=5 ) = ^(17)C_5 * (60\%)^5 * (1 - 60\%)^(17-5) = 0.008072842`

So, we have:

`P(x \le 5) = 1.71798692*10^(-7)+0.00000438086+0.00005257039+0.00039427799+0.00206995948+0.008072842`

`P(x \le 5) = 0.01059420251`

`P(x \le 5) = 0.0110`