The weight of certain brand of candies are normally distributed with a mean weig

Question

The weight of certain brand of candies are normally distributed with a mean weight of 0.5649 g and a standard deviation of 0.0619 g. A sample of three candles come from a package containing 465 candles, and the package label the net weight is 288.5 g. (If every package has 455 candies, the mean weight of the candies must exceed 388.5/455 = 0.8538 g for the net contents to weigh at least 365.5 g) a. If 1 candy is randomly selected, find the probability that it weighs more than g. The probability is _____. (Round to four decimal places as needed.) If 455 candles are randomly selected, find the probability that their mean weight is at least 0.8598 g. The probability that a sample of 455 candies will have a mean of g. or greater is _____. (Round to four decimal places as needed.) c. Given these results, does it that the candy company to providing consumers with the amount claimed on the label? _______ because the probability of getting a sample mean of 0.8538 g or greater when 455 candies are selected (2) _____ exceptionally small. Yes, No, is is not

Explanation / Answer

a) given mean = 0.8638

standard deviation = 0.0519

x^=0.8549

Z = (X^ - )/      or       Z = (.8549 - .8638)/.0519 = -0.0171

The area to the right of this Z-score from standard z table translates to a probability of 0.5040

Part b)we will caluclate with a sample standard deviation:

number of candles is n =455

x = /n = .0519/(455) = 0.0024

Z = (.8549 - .8638)/.0024 = -3.7083

The area to the right of this Z-score from standard z table translates to a probability of is its >3.4 so the probability will be 1

c)  Yes, because the probability of getting a sample mean of 0.8549 or greater when 441 candies are selected is NOT exceptionally small.

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