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.

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, Z_0.048 =(150-μ)/σ

                 -1.66 =(150-μ)/σ

 μ -1.66σ = 150 …………….1

Also, Z_0.1 =(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.)