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2011-02-22 2:39 am

Q1) Given 5 integers: 45,47,48,49,x. If the standard deviation is 1.6, find the value of x and the mean of all these integers.
ans:45,46.8Q2) A factory produces a machine components with an average length of 3.5cm and a standard deviation of 0.01cm. The tolerance limit for the lengths of the machine components is 3.5+or-0.02cm. Assuming that the lengths of the machine components are normally distributed.a) find the % of machine components whose lengths lie
i)between 3.48cm and 3.51cm,
ii)outside the tolerance limit.b) If a worker make a mistake so that machine components with an average length of 3.51cm and a standard deviation of 0.01cm are produced, find the % of machine components whose lengths lie outside the tolerance limit.
ans: 81.5%,5%,16.25%

回答 (1)

良師益友

2011-02-23 12:07 am

✔ 最佳答案

Answers as follows:

1) Actually it seems out of syllabus, but you can solve in the following ways:

Mean ( M ) = ( 45 + 47 + 48 + 49 + x ) / 5

Mean ( M ) = ( 189 + x ) / 5

Mean ( M ) = 37.8 + 0.2x

Use Square of S.D. ( i.e. Variance )

( 1.6 )^2 = [ ( 45 - M )^2 + ... + ( x - M )^2 ] / 5

( 7.2 - 0.2x )^2 + ( 9.2 - 0.2x )^2 .. + ( 37.8 - 0.8x )^2 = 12.8

Solving this step, we have x = 45 ( -ve rej. )

Mean = 37.8 + 0.2( 45 )

Mean = 46.8
==========

2)

(a)(i) Req. %

= 1/2 ( 68% ) + 1/2 ( 95% ) [ i.e. from -2 S.D. to 1 S.D. ]

= 81.5%
=======

(a)(ii) Req %

= 1 - 95% [ i.e. out of 2 S.D. +/- 2 ]

= 5%
=====

(b) Req %

= 1/2 ( 1 - 99.5% ) + 1/2 ( 1 - 68% ) [ i.e. those < -3 S.D. and > 1 S.D. ]

= 16.25 %
========

Hope I can help you.

參考: Mathematics Teacher Mr. Ip

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