4. Questions 6b and c of January 2008 on this link:
http://www.xtremepapers.net/Edexcel/Advanced%20Level/Mathematics/2008%20Jan/6683_01_que_20080115.pdf
(6) (b)Weights between 190 and 210 are 60 %.
Now 60 % is equal to 0.6 of the probability right. So find out the value of
si (0.6) which is equal to 0.7257 .
Now you know the formula :
X - mean
Z = -------------
standard deviation
Let standard deviation be
s.
So :
210 - 200 190 - 200
------------ - ------------ = 0.7257
s s
10 - (-10)
----------- = 0.7257
s
20 = 0.7257s
s = 20/(0.7257)
standard deviation = 27.55959763 (or 27.56)
(c)Use the same formula of normal distribution.
If you will use the original value of
standard deviation (that is
27.55959763 and not 27.56), you will be benefited.
180 - 200
---------------
27.55959763
= si (-0.7257)
= 1 - { si (0.726) }
= 1 - 0.766
= 0.234
So
0.234 is the probability that the customer will complain.