(a) Assume that the number of vehicles that pass through a tire repair shop during 9:00 A.M. and 9:30 A.M. on any day has the probability distribution given in Table 1.

Table 1. List the probability distribution

No. of Vehicles (V)

10

11

12

13

14

15

Probability P(V=v)

0.17

k

0.25

0.12

0.13

0.12

Find

(i) the value of k

(ii) the probability if at least 13 vehicles pass through the tire repair shop.

(iii) the probability if at most 12 vehicles pass through the tire repair shop.

(iv) the probability if exactly 16 vehicles pass through the tire repair shop.

(b) Let a function (V) = 21 represents the amount of money, in dollars, paid to the attendant by the manager. What will be the expected earning for attendant at this particular time period for any day?