Question

Nutty Chocolate candy has real nuts covered with chocolate. The typical weight of the nuts in a package is normally distributed with a mean of $12$ grams and a standard deviation of $.8$ grams. The thick chocolate coating is also normally distributed with a mean weight of $5$ grams and a standard deviation of $.65$ grams. Nutty Chocolate candies come in a package of $20$ candies to a bag. What is the mean of the weight of a bag of Nutty Chocolate candies?

• A. $280$ gm
• B. $320$ gm
• C. $340$ gm
• D. None of these

Answer 1

The correct option is C $340$ gm

Given that weight of nuts in a package is normally distributed with a mean of $12$ gms. and

standard deviation of $0.8$ gms.

Given that thick chocolate coating is normally distributed with a mean of $5$ gms. and

standard deviation of $0.65$ gms.

Therefore, the weight of the candy is $12+5=17$ gms.

Standard deviation of the candy is $\sqrt{{0.8}^2+{0.65}^2}=1.031$ gms.

Total number of candies in a package is $20$

Therefore, the average package weight is $20(12+5)=20\ast 17=340$ gms.