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 9.5 kilograms?

Answer 1

Solution:-

Given that,

x = 9.5

standard deviation = = 0.055

Using standard normal table,

P(Z < z) = 1%

= P(Z < z) = 0.01

= P(Z < -2.326) = 0.01   

z = -2.326

Using z-score formula,

x = z * +

9.5 = -2.326 * 0.055 +

= 9.5 - (-2.326 * 0.055)

= 9.6 kilograms