Question

a) The average daily sales of 500 branch offices was Ksh 150000 with a standard deviation of Ksb 15000. Assuming that the sales are normally distributed, determine how many branches have sales between: i. 120000 and 145000 shillings 140000 and 165000 shillings b) Describe the term game theory and describe at least three types of games C) Reduce the following game by Dominance and find the game value. TABLE 1 PLAYER B 11 III IV IN 3 4 lo PLAYER A Im -- IN It It MI IN 4 4 lo lo 4 O

Answer 1

a.

If X is the daily sales

then X follows normal distribution with a mean = 150000 and Std deviation= 15000

i. No of branches with sales between 120000 & 145000

When X= 120000, Z= (X-mean)/Standard deviation

X =120000 : Z = -2

X= 145000 :Z = -0.33

Now, we calculate P(-2<=Z<=-0.33)= P(0.33<=Z<=2)=P(Z<=2)-P(Z<=0.33)=0.97725-0.62930=0.34795 (From Normal Tables)

Multiplying the probability with 500 to get the number of offices = 500*0.34795= 173.975 or 174 offices approximately.

ii.140000 & 165000

Applying a similar procedure:

X= 140000: Z= -0.66

X= 165000: Z= 1

Now, we calculate P(-0.66<=Z<=1)= P(-0.66<=Z<=0)+P(0<=Z<=1)=0.24537+0.34134=0.58671 (From Normal Tables)

Multiplying the probability with 500 to get the number of offices = 500*0.58671= 293.355 or 293 offices approximately.