Question

Areal estate agent has 18 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling anyone property is independent of selling another property. Compute the probability of selling more than 4 properties in one week, Round your answer to four decimal places.

Answer 1

X ~ Bin ( n ,p)

Where n = 18 , p = 0.80

Using Normal Approximation to Binomial
Mean = n * P = ( 18 * 0.5 ) = 9
Variance = n * P * Q = ( 18 * 0.5 * 0.5 ) = 4.5
Standard deviation = √(variance) = √(4.5) = 2.1213

P(X < x) = P(Z < ( x - mean) / SD )

With continuity correction)

P(X > 4) = P(X > 4.5)

P ( X > 4.5 ) = P(Z > (4.5 - 9 ) / 2.1213 )
= P ( Z > -2.12 )
= 1 - P ( Z < -2.12 )
= 1 - 0.0170
= 0.9830