The weights of a certain brand of candies are normally distributed with a mean weight of 0.8552 g and a standard deviation of 0.0519 g. A sample of these candies came from a package containing 442 candies, and the package label stated that the net weight is 377.3 g. (If every package has 442 candies, the mean weight of the candies must exceed StartFraction 377.3 Over 442 EndFraction equals0.8537 g for the net contents to weigh at least 377.3 g.) a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8537 g. The probability is nothing. (Round to four decimal places as needed.)

The probability that the weight of a candy randomly selected is more than 0.8537 is 0.7486

Step-by-step explanation:

The given parameters are;

The mean candle weight = 0.8552 g

The standard deviation = 0.0519 g

The number in the sample, n = 442 candles

By central limit theorem, the sample standard deviation, is given by the relationship;

The probability is given by the relation;

The from the z-score table we have = 0.2514

The probability of P (z > -6076) = 1 - 0.2514 =  0.7486

The probability that the weight of a candy randomly selected is more than 0.8537 = 0.7486.

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