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?

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.

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)