Question

A wildlife conservationist specializing in wolf conservation read an article from 2008 that claimed that the number of wolves born in a litter is normally distributed with a mean of 4.8 puppies and a standard deviation of 1.2 puppies. a. From the information above, what proportion of wolf litters will have more than 6 puppies? Round answer to 3 significant digits.

Answer 1

Given Mean $\mu$ = 4.8 puppies

Standard Deviation $\sigma$ = 1.2 puppies

We need to find proportion of wolf litters that have will have more than 6 puppies

P(X > 6)

z-score = (X - $\mu$ ) / $\sigma$

= (6 - 4.8) / 1.2

= 1.2 / 1.2

= 1

The area to the left of z-score will give us P(X < 6) here

P(X < 6) = 0.84134 from below attached table

we know that P(X < 6) + P(X > 6) = 1

P(X > 6) = 1 - P(X < 6)

= 1 - 0.84134

= 0.15866

proportion of wolf litters that have will have more than 6 puppies = 0.15866

= 0.159 rounded to 3 decimal places   

5430 STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. 2 .00 .01 .04 .05 .06 .07 .09 0.0 .50000 50199 .50798 51197 51595 51994 .52392 .52790 .53188 .53586 0.1 53983 .54776 55172 55567 S5962 56356 56749 57142 .57535 .57926 .58317 .58706 59095 59483 59871 .60257 .60642 .61026 .61409 0.3 .61791 .62172 .62552 62930 63307 63683 .64058 .64431 .64803 65173 0.4 65542 .65910 66276 66610 .67003 67364 .67724 .68082 .68439 .68793 0.5 .69146 69497 .70194 .70540 .70884 .71226 .71566 .71904 .72240 0.6 .72575 .72907 73237 .73565 .73891 74215 74537 74857 75175 .75490 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524 0,8 .78814 .79103 .79389 .79673 .79955 80234 80511 .80785 81057 .81327 0.9 .81594 .81859 .82121 82381 82639 .82894 .83147 .83398 .83646 .83891 1.0 .84134 .84375 .84614 84849 85083 .85314 85543 .85769 .85993 .86214 1.1 .86433 .86650 .86864 87076 87286 .87493 .87698 .87900 .88100 .88298 1.2 .88493 .88686 .88877 89065 89251 89435 .84617 .89796 .89973 .90147 1.3 .90320 .90490 90658 90824 90988 91149 91309 91466 91621 91774 91924 92073 92220 .92364 92507 92647 .92785 .92922 93056 .93189 1.5 93319 93448 93574 93699 93822 93943 94062 94179 94295 .94408 1.6 .94520 .94630 94738 .94845 94950 95053 .95154 95254 .95352 .95449 1.7 .95543 .95637 95728 95818 95907 95994 96080 96246 96327 1.8 .96407 196485 96562 96638 -96712 96784 .96856 196926 .96995 97062 1,9 97128 97193 97257 97320 97381 97441 97500 97558 97615 .97670 2.0 .97725 .97778 97831 97882 .97932 97982 98030 98077 98124 .98169 2.1 .98214 98257 98300 98341 98382 98422 98461 98500 .98537 98574 2.2 .98610 .98645 98679 98713 .98745 98778 .98809 98840 .98870 .98499 .98928 .98956 98983 99010 .99036 99061 99086 .99134 .99158 2.4 99180 .99202 99245 99266 99286 99305 99343 99361 2.5 .99379 .99396 .99413 .99430 .99446 .99461 .99477 .99492 99506 .99520 2.6 99534 .99547 99560 99573 99585 99598 99609 99621 99632 99643 2.7 99653 99664 99674 .99693 .99702 .99711 .99720 99728 .99736 2.8 99744 .99752 .99760 99767 99774 99781 99788 99795 99801 99807 2.9 .99813 .99819 .99825 99201 .99836 99841 .99846 99851 99856 .99861 3.0 99863 99869 99874 99878 99882 99886 99889 99893 99896 99900 99903 .99906 99910 99913 99916 99918 99921 99924 99926 .99929 .99931 .99934 99936 .99938 .99940 .99942 99944 99948 .99950 99952 99953 99955 99957 99958 99960 99961 99962 99964 99965 3.4 .99966 .99968 99969 .99970 .99971 99972 .99973 .99974 99975 99976 3.5 99972 .99978 99978 99979 99980 99981 99981 99982 99983 99983 3.6 99984 .99985 99985 99986 .99986 99987 .99987 .99988 .99988 .99989 99989 .99990 99990 99990 99991 99991 99992 99992 3.8 99993 .99993 .99993 99994 99994 99994 99994 99995 99995 .99995 3.9 .99995 .99995 .99996 99996 .99996 .99996 .99997 .99997 99683