3. A machine for filling cereal boxes roughly follows a Normal distribution. a)

Question

3. A machine for filling cereal boxes roughly follows a Normal distribution.
a) Suppose the machine has a standard deviation of 1 ounce of fill per box. What setting for the mean ounces of
fill per box will allow 16 ounce boxes to overflow only 1% of the time?
b) Suppose instead that the standard deviation is not known, but can be fixed at certain levels by adjusting the
machine. What is the largest value of that will allow the actual value dispensed to be within 1 ounce of the
mean with probability at least 0.95?

3. A machine for filling cereal boxes roughly follows a Normal distribution a) Suppose the machine has a standard deviation of 1 ounce of fill per box. What setting for the mean ounces of fill per box will allow 16 ounce boxes to overflow only 1% of the time? b) Suppose instead that the standard deviation is not known, but can be fixed at certain levels by adjusting the machine. What is the largest value of that will allow the actual value dispensed to be within 1 ounce of the mean with probability at least 0.95?

Explanation / Answer

Ans:

a)z=(x-mean)/std dev

P(Z>=z)=0.01

P(Z<=z)=1-0.01=0.99

z=2.33

2.33=(16-mean)/1

mean=16-2.33=13.67

b)

z value for 95% CI are +/-1.96

1.96=1/std dev

standard deviation=1/1.96

std dev=0.51

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