use excrel only show all codes 2 The daily consumption of wa

use excrel only. show all codes

2. The daily consumption of water in millions of gallons in a certain city can be treated as a random variable having a gamma distribution with 4 and -3. If the water tower of this city has a daily capacity of 12 million gallons find (a) the probability that this water supply will be inadequate on any given day (b) the probability that this water supply will be adequate on any given day if the daily capacity is changed to 13, 14, 15, 16, and 17 million gallons. You must show the Excel/Matlab programming statements for your answers.

Solution

a) =1 - GAMMA.DIST(12, 4, 3, TRUE)

= 0.43347

b) Adequate if daily capacity is 13

=GAMMA.DIST(13, 4, 3, TRUE)

= 0.628809

Daily capacity is 14

=GAMMA.DIST(14, 4, 3, TRUE)

= 0.685039

Daily capacity is 15

=GAMMA.DIST(15, 4, 3, TRUE)

= 0.734974

Daily capacity is 16

=GAMMA.DIST(16, 4, 3, TRUE)

= 0.778689

Daily capacity is 17

=GAMMA.DIST(17, 4, 3, TRUE)

= 0.816482