Question

The weights of bags filled by a machine are normally distributed with a standard deviation of 0.055 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 10.5 kilograms? Round the answer to 2 decimal places.

Answer 1

Answer:

Step-by-step explanation:

Given that the  weights of bags filled by a machine are normally distributed with a standard deviation of 0.055 kilograms and a mean that can be set by the operator.

Let the mean be M.

Only 1% of the bags weigh less than 10.5 kilograms

i.e. P(X<10.5) = 0.01

corresponding Z value for P(Z<z) = 0.01 is -0.025

i.e. 10.5 = M-0.025(0.055)

Solve for M from the above equation

M = $10.5+0.025(0.055)\\=10.501375$

Rounding off we get

10.50 kgs

Mean weight should be fixed as 10.50 kg.