Question

A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg).If the manager’s belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?

a) 740 mg to 780 mgb) 700 mg to 740 mgc) 680 mg to 720 mgd) 660 mg to 720 mge) 620 mg to 660 mg

Answer 1

b) 700 mg to 740 mg

Explanation:

The mean is the sum of all the samples divided by the quantity of the samples, so a mean is a number between the maximum and the minimum sample. In this case, 720 mg must be in the interval, so letter a and e are eliminated.

The mean also represents the proportion of the samples, because the samples intend to be close to the mean. So, if 720 mg is the maximum or the minimum sample weight, it means that there are many samples close to it, and the proportion of the distribution will be small. So, letter c and d can't be the answer.

So, the largest proportion of weights is given in letter b, the interval of weights must be 700 mg to 740 mg.