In a certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with a=4 and ß= 2. If the daily capacity of that city is 6 million liters of water, what is the probability that on any given day the water supply is inadequate? Click the icon to view the Incomplete Gamma Function table. The probability is (Round to three decimal places as needed.) Incomplete Gamma Function table T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 0.9980 0.9990 1.0000 The Incomplete Gamma Function: F(x; a) = le dy 1 3 4 5 6 7 8 9 10 2 0.6320 0.2640 0.0800 0.0190 0.0040 0.0010 0.0000 0.0000 0.0000 0.0000 0.8650 0.5940 0.3230 0.1430 0.0530 0.0170 0.0050 0.0010 0.0000 0.0000 0.9500 0.8010 0.5770 0.3530 0.1850 0.0840 0.0340 0.0120 0.0040 0.0010 0.9820 0.9080 0.7620 0.5670 0.3710 0.2150 0.1110 0.0510 0.0210 0.0080 0.9930 0.9600 0.9600 0.8750 0.7350 0.5600 0.3840 0.2380 0.1330 0.0680 0.0320 0.9830 0.9380 0.8490 0.7150 0.5540 0.3940 0.2560 0.1530 0.0840 0.9930 0.9700 0.9180 0.8270 0.6990 0.5500 0.4010 0.2710 0.1700 0.9970 0.9860 0.9580 0.9000 0.8090 0.6870 0.5470 0.4070 0.2830 0.9990 0.9940 0.9790 0.9450 0.8840 0.7930 0.6760 0.5440 0.4130 1.0000 0.9970 0.9900 0.9710 0.9330 0.8700 0.7800 0.6670 0.5420 0.9950 0.9850 0.9620 0.9210 0.8570 0.7680 0.6590 0.9980 0.9920 0.9800 0.9540 0.9110 0.8450 0.7580 0.9990 0.9960 0.9890 0.9740 0.9460 0.9000 0.8340 0.9940 1.0000 0.9980 0.9860 0.9680 0.9380 0.8910 0.9990 0.9820 0.9630 0.9970 0.9920 0.9630 0.9300 6 8 7 10 5 9 1 2 0.9990 1.0000 3 α 4 a D - X -
In a certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with a=4 and ß= 2. If the daily capacity of that city is 6 million liters of water, what is the probability that on any given day the water supply is inadequate? Click the icon to view the Incomplete Gamma Function table. The probability is (Round to three decimal places as needed.) Incomplete Gamma Function table T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 0.9980 0.9990 1.0000 The Incomplete Gamma Function: F(x; a) = le dy 1 3 4 5 6 7 8 9 10 2 0.6320 0.2640 0.0800 0.0190 0.0040 0.0010 0.0000 0.0000 0.0000 0.0000 0.8650 0.5940 0.3230 0.1430 0.0530 0.0170 0.0050 0.0010 0.0000 0.0000 0.9500 0.8010 0.5770 0.3530 0.1850 0.0840 0.0340 0.0120 0.0040 0.0010 0.9820 0.9080 0.7620 0.5670 0.3710 0.2150 0.1110 0.0510 0.0210 0.0080 0.9930 0.9600 0.9600 0.8750 0.7350 0.5600 0.3840 0.2380 0.1330 0.0680 0.0320 0.9830 0.9380 0.8490 0.7150 0.5540 0.3940 0.2560 0.1530 0.0840 0.9930 0.9700 0.9180 0.8270 0.6990 0.5500 0.4010 0.2710 0.1700 0.9970 0.9860 0.9580 0.9000 0.8090 0.6870 0.5470 0.4070 0.2830 0.9990 0.9940 0.9790 0.9450 0.8840 0.7930 0.6760 0.5440 0.4130 1.0000 0.9970 0.9900 0.9710 0.9330 0.8700 0.7800 0.6670 0.5420 0.9950 0.9850 0.9620 0.9210 0.8570 0.7680 0.6590 0.9980 0.9920 0.9800 0.9540 0.9110 0.8450 0.7580 0.9990 0.9960 0.9890 0.9740 0.9460 0.9000 0.8340 0.9940 1.0000 0.9980 0.9860 0.9680 0.9380 0.8910 0.9990 0.9820 0.9630 0.9970 0.9920 0.9630 0.9300 6 8 7 10 5 9 1 2 0.9990 1.0000 3 α 4 a D - X -
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 42E
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Transcribed Image Text:In a certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with a = 4 and B= 2. If the daily capacity of that city is 6 million liters of water, what is
the probability that on any given day the water supply is inadequate?
Click the icon to view the Incomplete Gamma Function table.
The probability is
(Round to three decimal places as needed.)
Incomplete Gamma Function table
CY
2
1
2
3
4
5
6
7
8
10
1
0.0000
2
9
0.6320 0.2640 0.0800 0.0190 0.0040 0.0010 0.0000 0.0000 0.0000
0.8650 0.5940 0.3230 0.1430 0.0530 0.0170 0.0050 0.0010 0.0000 0.0000
0.9500 0.8010 0.5770 0.3530 0.1850 0.0840 0.0340 0.0120
0.0120 0.0040 0.0010
0.3710 0.2150 0.1110
0.1110 0.0510 0.0210
0.5600 0.3840 0.2380
0.2380 0.1330
0.1330 0.0680
0.0680 0.0320
0.3940 0.2560 0.1530 0.0840
0.6990 0.5500 0.4010 0.2710 0.1700
3
4 0.9820 0.9080 0.7620 0.5670
0.9930 0.9600 0.8750 0.7350
0.9980 0.9830 0.9380 0.8490 0.7150 0.5540 0.3940
0.9990 0.9930 0.9700 0.9180 0.8270 0.6990 0.5500
1.0000
0.0080
0.9970 0.9860 0.9580 0.9000 0.8090 0.6870 0.5470 0.4070 0.2830
0.9990 0.9940 0.9790 0.9450 0.8840 0.7930 0.6760
0.6760 0.5440 0.4130
1.0000 0.9970 0.9900 0.9710 0.9330 0.8700 0.7800 0.6670 0.5420
5
67899
10
11
12
13
14
15
2
The Incomplete Gamma Function: F(x; a) = foy-le- dy
1
2
a
0.9990 0.9950 0.9850 0.9620 0.9210
0.9620 0.9210 0.8570 0.7680 0.6590
1.0000 0.9980 0.9920 0.9800 0.9540 0.9110 0.8450 0.7580
0.9990 0.9960
0.9460 0.9000 0.8340
0.9960 0.9890 0.9740
1.0000 0.9980 0.9940 0.9860 0.9680 0.9380 0.8910
0.9990
0.9820
0.9970 0.9920
0.9630 0.9300
8
10
5
6
7
9
3
4
a
-
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