A mass of 150g was hung in turn from 250 pieces of a certain yarn, and 12 of the pieces broke. A load of 200g was then hung from the previously unbroken pieces and a further 213 pieces broke. Assume that yarn strength is distributed normally. Estimate the mean and standard deviation of the yarn strength.

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The proportion of yarn that can withstand 150g of load, = 238/250 = 0.952

The proportion of yarn that cannot withstand = 1-0.952= 0.048 or 12/250 = 0.048

The proportion of yarn that can withstand 200g of load, = 25/250 = 0.1

Let µ and σ be mean and standard deviation of yarn’s strength

Therefore, Z0.048 =(150-μ)/σ

                 -1.66 =(150-μ)/σ

 μ -1.66σ = 150 …………….1

Also, Z0.1 =(200-μ)/σ

                 1.28 =(200-μ)/σ

 μ +1.28σ = 200 …………….2

From equation 1 & 2, µ =178.23g (Approx.) and σ =17g (Approx.)

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