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1. Suppose that the annual rainfall in Southern California is normally approximated with mean 8 (in) and variance 4 (in²). a. Determine the probability that the amount of rainfall of the coming year is one standard deviation below the mean. b. Determine the minimum amount of rainfall for a given year to be in the top 5%.

1. Suppose that the annual rainfall in Southern California is normally approximated with mean 8 (in) and variance 4 (in²). a. Determine the probability that the amount of rainfall of the coming year is one standard deviation below the mean. b. Determine the minimum amount of rainfall for a given year to be in the top 5%.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. Suppose that the annual rainfall in Southern California is normally approximated with mean 8 (in) and variance 4 (in²). a. Determine the probability that the amount of rainfall of the coming year is one standard deviation below the mean. b. Determine the minimum amount of rainfall for a given year to be in the top 5%. 2. Suppose that the life-time of a certain printer follows an exponential distribution with mean 2 years. Suppose that a printer has been in used for 3 years, determine the probability that it will last at least 2 more years.
Transcribed Image Text:1. Suppose that the annual rainfall in Southern California is normally approximated with mean 8 (in) and variance 4 (in²). a. Determine the probability that the amount of rainfall of the coming year is one standard deviation below the mean. b. Determine the minimum amount of rainfall for a given year to be in the top 5%. 2. Suppose that the life-time of a certain printer follows an exponential distribution with mean 2 years. Suppose that a printer has been in used for 3 years, determine the probability that it will last at least 2 more years.
STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .06 .07 .08 .03 51197 .55172 -59095 .00 .01 .02 .04 .05 0.0 -50000 .50399 .50798 51595 51994 52392 52790 53188 0.1 53983 .54380 .54776 .55567 55962 .56356 .56749 57142 0.2 57926 .58317 58706 59483 59871 .60257 .60642 .61026 0.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 0.4 .65542 .65910 .66276 66640 .67003 .67364 0.5 .69146 .69497 .69847 .70194 .70540 .70884 0.6 .72575 .72907 .73237 .73565 .73891 .74215 0.7 .75804 .76115 .76424 .76730 .77035 .77337 0.8 .78814 .79103 .79389 .79673 .79955 .80234 0,9 .81594 .81859 .82121 .82381 .82639 82894 1.0 .84134 .84375 .84614 .84849 .85083 .85314 1.1 .86433 .86650 .86864 .87076 .87286 .87493 1.2 .88493 .88686 .88877 .89065 .89251 .89435 1.3 .90320 .90490 .90658 .90824 .90988 91149 .91309 91924 92073 92220 92364 92507 92647 92785 92922 93056 1.5 .93319 .93448 93574 .93699 .93822 .93943 .94062 .94179 94295 1.6 94520 94630 .94738 94845 .94950 95053 .95154 .95254 95352 1.7 95543 .95637 .95728 .95818 .95907 95994 .96080 96164 96246 1.8 .96407 .96485 .96562 .96638 96712 .96784 .96856 .96926 .96995 1.9 97128 97193 97257 .97320 97381 97441 97500 .97558 97615 2.0 .97725 .97778 97831 97882 .97932 .97982 98030 .98077 98124 2.1 98214 98257 .98300 98341 .98382 .98422 98461 .98500 .98537 2.2 .98610 .98645 .98679 98713 98745 98778 .98809 .98840 .98870 2.3 .98928 98956 .98983 .99010 .99036 .99061 .99086 .99111 .99134 2.4 .99180 .99202 99224 99245 .99266 99286 99305 99324 99343 2.5 .99379 .99396 99413 .99430 .99446 .99461 .99477 99492 2.6 .99534 .99547 .99560 .99585 2.7 .99693 .67724 .68082 .68439 .71226 .71566 .71904 .74537 .74857 .75175 .77637 .77935 .78230 .80511 .80785 .81057 83147 .83398 .83646 .85543 .85769 85993 .87698 .87900 .88100 .89617 .89796 .89973 .91466 91621 .98899 .99158 .99361 .99506 .99520 .99609 .99621 99632 99643 .99598 .99702 .99728 .99736 99711 .99720 .99788 .99795 .99801 99774 .99807 .99851 99856 .99861 99781 99841 99846 99886 99889 99893 99896 .99900 99918 .99921 .99924 99926 .99929 .99573 .99653 .99664 99674 99683 2.8 99744 .99752 .99760 99767 2.9 99813 99819 99825 .99831 .99836 3.0 .99865 .99869 99874 99878 .99882 3.1 .99903 .99906 .99910 .99913 .99916 3.2 .99931 .99934 .99936 .99938 .99940 99942 .99944 .99946 .99948 .99950 3.3 99952 99953 99955 .99957 99958 .99960 .99961 .99962 99964 99965 99966 99968 99969 99970 .99971 99972 .99973 .99974 .99975 99976 3.5 99977 .99978 .99978 99979 99980 99981 99981 99982 99983 99983 3.6 99984 99985 .99985 99986 99986 99987 99987 .99988 99988 99989 3.7 99989 .99990 .99990 99990 99991 99991 99992 .99992 99992 99992 3.8 99993 99993 .99993 99994 99994 99994 99994 .99995 99995 99995 3.9 99995 99995 .99996 99996 99996 99996 99996 .99996 99997 .99997 .09 53586 .57535 .61409 .65173 .68793 .72240 .75490 .78524 .81327 .83891 .86214 .88298 .90147 91774 93189 .94408 .95449 .96327 97062 .97670 .98169 98574
Transcribed Image Text:STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .06 .07 .08 .03 51197 .55172 -59095 .00 .01 .02 .04 .05 0.0 -50000 .50399 .50798 51595 51994 52392 52790 53188 0.1 53983 .54380 .54776 .55567 55962 .56356 .56749 57142 0.2 57926 .58317 58706 59483 59871 .60257 .60642 .61026 0.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 0.4 .65542 .65910 .66276 66640 .67003 .67364 0.5 .69146 .69497 .69847 .70194 .70540 .70884 0.6 .72575 .72907 .73237 .73565 .73891 .74215 0.7 .75804 .76115 .76424 .76730 .77035 .77337 0.8 .78814 .79103 .79389 .79673 .79955 .80234 0,9 .81594 .81859 .82121 .82381 .82639 82894 1.0 .84134 .84375 .84614 .84849 .85083 .85314 1.1 .86433 .86650 .86864 .87076 .87286 .87493 1.2 .88493 .88686 .88877 .89065 .89251 .89435 1.3 .90320 .90490 .90658 .90824 .90988 91149 .91309 91924 92073 92220 92364 92507 92647 92785 92922 93056 1.5 .93319 .93448 93574 .93699 .93822 .93943 .94062 .94179 94295 1.6 94520 94630 .94738 94845 .94950 95053 .95154 .95254 95352 1.7 95543 .95637 .95728 .95818 .95907 95994 .96080 96164 96246 1.8 .96407 .96485 .96562 .96638 96712 .96784 .96856 .96926 .96995 1.9 97128 97193 97257 .97320 97381 97441 97500 .97558 97615 2.0 .97725 .97778 97831 97882 .97932 .97982 98030 .98077 98124 2.1 98214 98257 .98300 98341 .98382 .98422 98461 .98500 .98537 2.2 .98610 .98645 .98679 98713 98745 98778 .98809 .98840 .98870 2.3 .98928 98956 .98983 .99010 .99036 .99061 .99086 .99111 .99134 2.4 .99180 .99202 99224 99245 .99266 99286 99305 99324 99343 2.5 .99379 .99396 99413 .99430 .99446 .99461 .99477 99492 2.6 .99534 .99547 .99560 .99585 2.7 .99693 .67724 .68082 .68439 .71226 .71566 .71904 .74537 .74857 .75175 .77637 .77935 .78230 .80511 .80785 .81057 83147 .83398 .83646 .85543 .85769 85993 .87698 .87900 .88100 .89617 .89796 .89973 .91466 91621 .98899 .99158 .99361 .99506 .99520 .99609 .99621 99632 99643 .99598 .99702 .99728 .99736 99711 .99720 .99788 .99795 .99801 99774 .99807 .99851 99856 .99861 99781 99841 99846 99886 99889 99893 99896 .99900 99918 .99921 .99924 99926 .99929 .99573 .99653 .99664 99674 99683 2.8 99744 .99752 .99760 99767 2.9 99813 99819 99825 .99831 .99836 3.0 .99865 .99869 99874 99878 .99882 3.1 .99903 .99906 .99910 .99913 .99916 3.2 .99931 .99934 .99936 .99938 .99940 99942 .99944 .99946 .99948 .99950 3.3 99952 99953 99955 .99957 99958 .99960 .99961 .99962 99964 99965 99966 99968 99969 99970 .99971 99972 .99973 .99974 .99975 99976 3.5 99977 .99978 .99978 99979 99980 99981 99981 99982 99983 99983 3.6 99984 99985 .99985 99986 99986 99987 99987 .99988 99988 99989 3.7 99989 .99990 .99990 99990 99991 99991 99992 .99992 99992 99992 3.8 99993 99993 .99993 99994 99994 99994 99994 .99995 99995 99995 3.9 99995 99995 .99996 99996 99996 99996 99996 .99996 99997 .99997 .09 53586 .57535 .61409 .65173 .68793 .72240 .75490 .78524 .81327 .83891 .86214 .88298 .90147 91774 93189 .94408 .95449 .96327 97062 .97670 .98169 98574
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