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