Question

Daily sales of theatre tickets at your cinema depend on the weather. probability sales Warm .50 $800 Cold .20 $1200 Rainy .20 $1600 Snowy .10 $1000 a. Calculate the expected daily sales. b. Calculate the variance of daily sales. c. Calculate the standard deviation of daily sales.

Answer 1

1060 ; 96400 ; 310.48

Explanation:

Given that:

P(X): __0.50 ___0.20 ____ 0.20 ____ 0.10

X : ___800 ___ 1200 ____ 1600 ____ 1000

The expected sales (m) : Σ(p * p(x))

(0.50 * 800) + (0.20 * 1200) + (0.20 * 1600) + ( 0.10 * 1000) = 1060

B.) variance (Var X) :

Σx²p - m²

(800^2*0.50) + (1200^2 * 0.20) + (1600^2 * 0.20) + (1000^2 * 0.10)] - m²

1220000 - 1060^2

= 96,400

Standard deviation = √variance

= √96400

= 310.48