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 mg
b) 700 mg to 740 mg
c) 680 mg to 720 mg
d) 660 mg to 720 mg
e) 620 mg to 660 mg

Answer 1

Option B.

Explanation:

It is given that the weight of candies is approximately normally distributed with mean 720 milligrams (mg).

It means most of the candies weight lies around the 720 milligrams.

In normal distribution,

Interval = Mean ± n × (standard deviation)

Where, n=1 for 68%, n=2 for 95% and n=3 for 99.7% and mean is the midpoint of the interval.

From the given option, only option B is true because 720 mg is the midpoint of 700 mg to 740 mg.

Therefore, the correct option is B.

Answer 2

option (b) 700 mg to 740 mg

Explanation:

Data provided;

The weight of candies is approximately normally distributed with mean 720 milligrams (mg)

this means that the most of the candies weight lies around the 720 milligrams

i.e

the most of the weight will be distributed as:

Mean ± standard deviation

here, the mean is 720 milligrams

thus,

the weights will lie within the range of some standard deviation above and below the mean and this is justified by the option (b) 700 mg to 740 mg

Hence,

the correct answer is option (b) 700 mg to 740 mg