Question

The machine described has standard deviation σ that can be fixed at certain levels by carefully adjusting the machine. What is the largest value of σ that will allow the actual amount dispensed to fall within 1 ounce of the mean with probability at least .95?

Answer 1

σ = 0.5102

Explanation:

If

Y = volume filled,

µ = mean

It is a normal distribution

It follows that

0.95 = P (|Y − µ| < 1) = P (|Z| < 1 / σ)

so that

1 / σ = 1.96 ⇒ σ = (1 / 1.96)

⇒ σ = 0.5102.