Question

1. 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.

Answer 1

Solution:

Let x be the weight of the booklet in the box and x's are independent and identically distributed. We are given:

The manufacturer is interested in calculating the probability that the 100 booklets weigh more than 100.4 ounces. We can write it as:

Using the central limit theorem we have:

Now to find the required probability, we have:

  

Now using the standard normal table, we have:

We have used the central limit theorem to find this probability