5. a, b easy.
a. standard deviation is 0. you need to understand the formula of SD on pg. 55 of the same book. you'll discover
![\Sigma](https://studentforums.biz/cgi-bin/mimetex.cgi?\Sigma)
x
2f /
![\Sigma](https://studentforums.biz/cgi-bin/mimetex.cgi?\Sigma)
f and
![\widetilde{x}](https://studentforums.biz/cgi-bin/mimetex.cgi?\widetilde{x})
, both equal 1, then only SD = 0.
b.
Ali => 12 * 1.07 = 12.84
Les => 16 * 0.76 = 12.16
Sam => 1 * 1 = 1
Therefore Ali is a clear winning, having caught highest mass of fish/
c.
Create a table for Sam's catch
Let 3rd fish caught be " a "
x x f x
2 f
1 1 1
1 1 1
a a a
2![\Sigma](https://studentforums.biz/cgi-bin/mimetex.cgi?\Sigma)
xf = 2+x
![\Sigma](https://studentforums.biz/cgi-bin/mimetex.cgi?\Sigma)
x
2 f = 2 + x
2![\widetilde{x}](https://studentforums.biz/cgi-bin/mimetex.cgi?\widetilde{x})
=
![\frac{2+x}{3} <br />](https://studentforums.biz/cgi-bin/mimetex.cgi?\frac{2+x}{3} <br />)
SD = 1
Using the SD formula and substituting the above values :
SD =
![\Sigma](https://studentforums.biz/cgi-bin/mimetex.cgi?\Sigma)
x
2 f /
![\Sigma](https://studentforums.biz/cgi-bin/mimetex.cgi?\Sigma)
xf -
root sign can be eliminate as SD = 1
1 = 2+x
2/ 2+x - (2+x/3)^ 2
simplify the eqn to get
2x
2 -4x -7 = 0
solve this equation to get x= 3.12 and -1.12
omit the -ve ans so your ans = 3.12 kg
it ain't that complicated as it looks. i've tried my best to explain it well. go through the "theory" of variance and SD you'll figure.