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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?

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jolis1796

Answer:

σ = 0.5102

Step-by-step 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.

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