Question

Despite lecturing your roommates on energy conservation, there is a 60% chance that the lights in a dorm room will be left on when nobody is home. Each day is independent. Suppose that, every day the light is left on in a dorm room, there are 1000 Watts of power used. Every day when the light is turned off, there are 200 Watts of power used. You keep track of X, the number of days the lights are left on over the next 30 days.

(a) Compute the expected amount of power used during the 30 days. (Give Answer only!)

(b) Compute the probability that 16,400 Watts (or more) of power are used during the 30 days. (Show detailed calculation and answer)

Answer 1

a.

E(no. of days lights on) = 30*P(lights on) = 30*0.60 = 18

E(noo. of days lights switched off) = 30 - E(no. of days lights on) = 30-18 = 12

E(power used) = 1000*E(no. of days lights on) + 200*E(no. of days lights switched off)

= 1000*18+200*12

= 20400 watts

E(power used) = 20400 watts

b.

for x days light left on :

total usage in month = 1000*x + 200*(30-x)

= 800*x + 6000

800x + 6000 >= 16400

8x + 60 >= 164

8x >= 104

x >= 13

P(lights left on on one day) = 0.60

x = no. of days lights left on

n=30

p=0.60

1-p = 0.40

P(x>=13) = P(13) + P(14) + ....+P(30)

= 0.9787

(PLEASE UPVOTE)