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 387.0​g.)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.)

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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 387.0​g.)

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.)
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Expert Answer

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

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Step 2

The required probability is ...

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