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StatisticsQ&A LibraryThe weights of a certain brand of candies are normally distributed with a mean weight of 0.8599 g and a standard deviation of 0.0519 g. A sample of these candies came from a package containing 453 candies, and the package label stated that the net weight is 387.0 g. (If every package has 453 candies, the mean weight of the candies must exceed 387.0/453=0.8542 g for the net contents to weigh at least 387.0g.)a. If 1 candy is randomly selected, find the probability that it weighs more than0.8542g.The probability is (Round to four decimal places as needed.)Question

Asked Apr 27, 2019

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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8599 g and a standard deviation of 0.0519 g. A sample of these candies came from a package containing 453 candies, and the package label stated that the net weight is 387.0 g. (If every package has 453 candies, the mean weight of the candies must exceed 387.0/453=0.8542 g for the net contents to weigh at least 387.0g.)

a. If 1 candy is randomly selected, find the probability that it weighs more than0.8542g.The probability is

(Round to four decimal places as needed.)

Step 1

__Solution__

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 ...

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