Question

The weights of bags filled by a machine are normally distributed with a standard deviation of 0.05 kg and a mean that can be set by the operator. At what level should the mean be set if it is required that only 1% of the bags weigh less than 10 kg?

Answer 1

`\mu` = 10.1163 kg

Explanation:

given data

σ = 0.05

x = 10

so we know here probability of x is 0.1 that is less than 10

so here Z is -2.326 by the standard table

we have here 1% to left when Z is - 2.326

now we apply relation between Z and x that is

Z =
`(x -\mu)/(\sigma )` .........1

put here value

-2.326 =
`(10 - \mu )/(0.05)`

`\mu` = 10.1163 kg