Question

REVIEW QUESTIONS Use this information for the following 3 questions The following is the probability distribution of a random variable x the demand for Christmas trees at our store in December: X 10 20 30 40 50 60 P(X) .10 25 .30 .20 .10 .05 We can purchase the trees at a wholesale price of $15 with a retail price of $25. Unsold trees are sold as firewood at $1 1. The standard deviation of X is: b. 31 C 13 d. 216 e. 19 lia0 What is P(Xs30)? a. 0.15 b. 0.25 c. 0.35 3 d. 0.65 e. 0.85 2. 0.3-P n-6 x:33 3. Find the optimal number of trees to stock at our tree store. a. 20 b. 30 с. 40 d. 50 e. 60

Answer 1

1. E(X)=$\sum xP(X=x)$= 10*.10+20*.25+30*.30+40*.20+50*.10+60*.05=31

E(X²)= 10^2*.10+20^2*.25+30^2*.30+40^2*.20+50^2*.10+60^2*.05=1130

V(X)=1130-31^2=169

SD(X)=13

2.P(X<=30)=P(X=10)+P(X=20)+P(X=30)=.10+.25+.30=.65

3. The optimum number is 40