Question

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8585 g and a standard deviation of 0.0523 g. A sample of these candies came from a package containing 467 candies, and the package label stated that the net weight is 398.8 g.​ (If every package has 467 candies, the mean weight of the candies must exceed 398.8/467=0.8539 g for the net contents to weigh at least 398.8 g.

a.) If 1 candy is randomly selected, find the probability that it weighs more than 0.8539 g.

b.) If 467 candies are randomly selected, find the probability that their mean weight is at least 0.8539 g.

c.) Given these results, does is seem that the candy company is providing consumers with the amount claimed on the label?

Answer 1

a)

Given,

= 0.8585 , = 0.0523

We convert this to standard normal as

P( X < x) = P( Z < x - / )

So,

P( X > 0.8539) = P( Z > 0.8539 - 0.8585 / 0.0523)

= P( Z > -0.0880)

= P( Z < 0.088)

= 0.5351

b)

Using central limit theorem,

P( < x) = P( Z < x - / / sqrt(n) )

So,

P( > 0.8539) = P( Z > 0.8539 - 0.8585 / 0.0523 / sqrt( 467) )

= P(Z > -1.9007)

= P( Z < 1.9007)

= 0.9713

c)

Yes, Since probability is not small, that is greater than 0.05.

It seem that the candy company is providing consumers with the amount claimed on the label.