GATE (TF) Textile 2011 Question Paper Solution | GATE/2011/TF/30

Question 30 (Textile Engineering & Fibre Science)

A yarn has mean strength of 10 N with a standard deviation of 1 N. The number of tests which must be conducted, so that at 95% confidence level, maximum error in the estimated mean strength is 1.96% is ____________________

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Given ,
Standard deviation( $\sigma$ )=1 N

Mean strength(x)=10 N

Maximum error in mean strength(S.E%)=1.96%

The number of tensts(N)=?

By formula-

$CV=\frac{\sigma}{x}\times 100$
$CV=\frac{1}{10}\times 100$
$CV=10$

$N=(\frac{1.96 \times CV}{S.E.})^2$

$N=(\frac{1.96 \times 10}{1.96})^2$

$N=(10)^2$
N=100 (Ans)

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