Question

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8541 g and a standard deviation of

0.0516 g. A sample of these candies came from a package containing 440 ​candies, and the package label stated that the net weight is 375.5 g.​ (If every package has 440 ​candies, the mean weight of the candies must exceed 375.5/440 =0.8534 g for the net contents to weigh at least 375.5 g.)

a. If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8541 g.

The probability is _______.

​(Round to four decimal places as​ needed.)

b. If 440 candies are randomly​ selected, find the probability that their mean weight is at least 0.8541 g.

The probability that a sample of 440 candies will have a mean of 0.8541g or greater is

______________.

​(Round to four decimal places as​ needed.)

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

Yes, because the probability of getting a sample mean of 0.8541g or greater when 440 candies are selected is not exceptionally small.

Answer 1

Answer :

Define : X : Weights of the certain brand of candies.

X ~ N ( 0,8541, 0.0516 )

a.

P ( X > 0.8541 ) = 0.5 ( Since oit is normal distribution and for Normal distroibution probabillity of either side of mean is 0.5)

b)

( Since mean remain same for the sampling distribution of sample mean )

In part b we have to find probability of sample mean is more than 0.8541

In this case we need to find the distribution of sample mean.

The distribution of sample mean is, If X has normal distribution with mean is and standard deviation is . If a random sample of size n ( n > 1) is drawn from the same distribution then sample mean has Normal distribution with mena is and standard deviation is .

c.

The given answer is correct.