Question

. Metropolitan Power and Light (MPL) tracks peak power usage, measured in gigawatts (GW), for its service area. MPL reports that in January peak daily demand for electrical power follows a normal distribution, with a mean of 4.3 GW and a standard deviation of .8 GW. (Note: A gigawatt is 1 billion watts of electricity, approximately the output of a nuclear fission reactor.) For a randomly selected January day:

a. There is a 30% probability that peak demand for electrical power will exceed_____ GW.

b. There is a 45% probability that peak demand will be between 4.0 GW. and _____ GW.

c. Suppose MPL wants to build a power generation capacity that will handle all but the very highest peak demands in January. Specifically, it wants to increase its capacity so that there is only a 1% probability that peak demand will exceed the new capacity. The company should build a generating capacity to meet a peak demand of _____ GW.

Answer 1

Ans:

Normal distribution with:

mean=4.3 GW

standard deviation= 0.8 GW

a)

P(Z>z)=0.3

P(Z<=z)=1-0.3=0.7

z=normsinv(0.7)=0.5244

x=4.3+0.5244*0.8

x=4.72

b)

z(4)=(4-4.3)/0.8=-0.375

P(-0.375<z<c)=0.45

P(z<c)-P(z<-0.375)=0.45

P(z<c)=0.45+0.3538=0.8038

c=normsinv(0.8038)=0.8553

x=4.3+0.8553*0.8

x=4.98

c)

P(Z>z)=0.01

P(Z<=z)=1-0.01=0.99

z=normsinv(0.99)=2.326

x=4.3+2.326*0.8

x=6.16 GW