STATISTICS PLEASE HELP

Question

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8541g and a standard deviation of 0.0525 g. A sample of these candies came from a package containing

467 candies, and the package label stated that the net weight is 398.6 g.​ (If every package has 467 candies, the mean weight of the candies must exceed 398.6/467=0.8535g for the net contents to weigh at least 398.6 g.)

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

0.8535 g.

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

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

0.8535 g.

​(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?

Answer 1

Here is part of the same problem with SLIGHTLY Different numbers! But the process is the same!

Step 1

Let X be the weight of a certain brand of candies and the weights are normally distributed with mean 0.8599 g and standard deviation 0.0519 g. A sample of one package of net weight 387.0 g contains 453 candies is taken.

Let X-bar be the sample mean and we have to find the probability that P(X-bar > 0.8542g).

Since the sample size n = 453 is large, by Central Limit Theorem, the sample mean is approximately normally distributed with

Step 2

The required probability is ...

https://www.bartleby.com/questions-and-answers/the-weights-of-a-certain-brand-of-candies-are-normally-distributed-with-a-mean-weight-of-0.8599-g-an/6fee708b-c475-429e-9973-cf72d51379c7