Question

3. A manufacturer of booklets packages them in boxes of 100. It is known that, on the average, a booklet weighs 30 grams, with a standard deviation of 1.5 grams. The manufacturer is interested in calculating Prob[100 booklets weigh more than 3.3 kg], a number that would help detect whether too many booklets are being put in a box. Explain how you would approximate the value of this probability reliably. Carefully describe your steps and indicate the use of any relevant theorems or assumptions. [5 marks]

Answer #1

Let random variable x denote the weights of a booklet

A manufacturer of booklets packages them in boxes of 100. It is
known that on the average, the booklets weight 1 ounce, with a
standard deviation of 0.05 ounces. The manufacturer is interested
in calculating the probability that the 100 booklets weigh more
than 100.4 ounces. Explain how you can approximate value of this
probability. Mention any relevant theorems or assumptions
needed.

a manufacturer packages bolts in boxes containing 100 each. Each
box of 100 bolts contains on average 6 defective bolts. The quality
control staff randomly selects a box at the end of the day from an
entire production run. What is the probability rounded to 4 decimal
places that the box will contain at most six defective bolts?

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