Question

A certain brand of candies have a mean weight of 0.8616g and a standard deviation of 0.0518 based on the sample of a package containing 447 candies. The package label stated that the net weight is 381.8g If every package has 447 candies the mean weight of the candies must exceed 381.8/447=0.8542 for the net contents to weight at least 381.8g.

a) if 1 candy is reandomly selected, find the probability that it weights more than 0.8542g. the probability is __

(round to four decimal places as needed)

b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.

the probability that a sample of 447 candies will have a mean of 0.8542g 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?

NO/YES because the probability of getting a sample mean of 0.8542g or greater when 447 candies are selected IS NOT/IS exceptionally small

Answer 1

a) if 1 candy is reandomly selected, find the probability that it weights more than 0.8542g. the probability is

z = (.8542 - .8616)/.0518 = -.142857

P(Z > -.142857) = .5568 (answer)

(round to four decimal places as needed)

b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.

the probability that a sample of 447 candies will have a mean of 0.8542g or greater is __

z = (.8542 - .8616)/(.0518/square root of 447 = -3.02034

P(Z > -3.02034) = .9987 (answer)

(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 0.8542g or greater when 447 candies are selected IS NOT exceptionally small