Question

The weights of bags filled by a machine are normally distributed with a standard deviation of 0.05 kilograms and a mean that can be set by the operator. At what level should the mean weight be set if it required that only 1% of the bags weigh less than 9.5 kilograms? Round the answer to 2 decimal places.

Answer 1

9.62 kg

Step-by-step explanation:

From a z-score table, P(z<-2.33) ≈ 0.01. So 9.5 should be 2.33 standard deviations below the mean.

z = (x − μ) / σ

-2.33 = (9.5 − μ) / 0.05

-0.1165 = 9.5 − μ

μ = 9.6165

Rounding to 2 decimal places, the mean should be set to 9.62 kg.