Question

The weights of bricks produced in a brick factory are normally distributed with a mean of 2 kg and a standard deviation of 0.1 kg. If the weight of a brick differs from 2 kg by more than 0.3 kg it is scrapped. Calculate the probability a randomly selected brick will have to be scrapped. (Correct to 4 decimal places).

Answer 1

Here mean = = 2kg

standard deviation = = 0.1 kg

If the weight of a brick differs from 2 kg by mora than 0.3 kg it is scrapped.

Let x is the weight of a random brick.

we have to find P(l x - 2l > 0.3 kg) = P(x > 2.3 kg) + P(x < 1.7 kg)

as the distriubtion is symmetric

P(l x - 2l > 0.3 kg) = 2 * P(x < 1.7 kg)

z = (1.7 - 2)/0.1 = -3

P(l x - 2l > 0.3 kg) = 2 * NORMSDIST(-3) = 2 * 0.00135 = 0.0027

so 0.27% of bricks would bescrapped.