Question

A mass of 150g was hung in turn from 250 pieces of a certain yarn,

and 12 of the pieces broke. A mass of 200 g then hung from the

previously unbroken pieces and further 213 pieces broke.

Assuming that yarn strength is distributed normally, estimate the

mean and standard deviation of the yarn’s strength.

Answer 1

This question presents a case where the sample size is $n=2$.

Let X be a random variable denoting the yarn strength.

Yarn strength is measured by the number of pieces that broke. As a result the random variable X assumes the number of broken pieces that is, $x=12, 213$

To find the mean, we apply the usual formula given as,

$\bar{x}=\sum(x)/n=(12+213)/2=112.5$

To determine the standard deviation, let us determine the variance first. Variance for the random variable X is given as,

$S^2=\sum(x-\bar{x})^2/(n-1)=20200.5/(2-1)=20200.5$

The standard deviation is,

$sd(X)=\sqrt{S^2}=\sqrt{20200.5}=142.1285$

Therefore, the mean is 112.5 and the standard deviation is 142.1285.