A certain brand of candies have a mean weight of 08613 g and

A certain brand of candies have a mean weight of 0.8613 g and a standard deviation of 0.0516.

A sample of these candies came from a package containing 470 candies, and the package label stated that the net weight is 401.0 g. (If every package has 470 candies, the mean weight of the candies must exceed 401.0 Over 470 EndFraction4010.8532g for the net contents to weigh at least 401.0 g.)

If 1 candy is randomly selected, find the probability that it weighs more than 0.8532g.

b. If 470 candies are randomly selected, find the probability that their mean weight is at least

0.8532g.

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

Solution

a)

You can figure this out by using a table of values of the standard normal distribution (a table of Z values).

z = (0.8613-0.8532)/0.0516 = 0.1569

From the table, you can find the probability of something falling within the range 0.8532-0.8613.

This is µ + 0.1569s.

The one-sided Z table will give you a value of 0.5636 for such an occurrence.

Therefore , 56.36% Answer

b)

The probability of candy being below the required weight is 0.4364 . ----->( (1- 0.5636), or use the z table calculator).

What are the chances that all 470 candies in the package will weigh less than 0.8532 g?

Therefore , (0.4363)^470 ~ 0 Answer

c)

Yes.