The weights of a certain brand of candies are normally distributed with a mean weight of 0.8557 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 446 candies, and the package label stated that the net weight is 380.8 g. (If every package has 446 candies, the mean weight of the candies must exceed 380.8/446 = 0.8539 g for the net contents to weigh at least 380.8 g.)
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8557 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 446 candies, and the package label stated that the net weight is 380.8 g. (If every package has 446 candies, the mean weight of the candies must exceed 380.8/446 = 0.8539 g for the net contents to weigh at least 380.8 g.)
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8557 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 446 candies, and the package label stated that the net weight is 380.8 g. (If every package has 446 candies, the mean weight of the candies must exceed 380.8/446 = 0.8539 g for the net contents to weigh at least 380.8 g.)
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8557 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 446 candies, and the package label stated that the net weight is 380.8 g. (If every package has 446 candies, the mean weight of the candies must exceed 380.8/446 = 0.8539 g for the net contents to weigh at least 380.8 g.)
Transcribed Image Text:The weights of a certain brand of candies are normally distributed with a mean weight of 0.8557 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 446 candies, and the package label stated that the net weight is 380.8 g. (If every package has 446 candies, the mean weight of the candies must exceed \( \frac{380.8}{446} = 0.8539 \) g for the net contents to weigh at least 380.8 g.)
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**a.** If 1 candy is randomly selected, find the probability that it weighs more than 0.8539 g.
The probability is \([ \; ]\).
*(Round to four decimal places as needed.)*
**b.** If 446 candies are randomly selected, find the probability that their mean weight is at least 0.8539 g.
The probability that a sample of 446 candies will have a mean of 0.8539 g 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?
\(\blacktriangledown\) because the probability of getting a sample mean of 0.8539 g or greater when 446 candies are selected is
\(\blacktriangledown\) exceptionally small.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
![The weights of a certain brand of candies are normally distributed with a mean weight of 0.8557 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 446 candies, and the package label stated that the net weight is 380.8 g. (If every package has 446 candies, the mean weight of the candies must exceed \( \frac{380.8}{446} = 0.8539 \) g for the net contents to weigh at least 380.8 g.)
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**a.** If 1 candy is randomly selected, find the probability that it weighs more than 0.8539 g.
The probability is \([ \; ]\).
*(Round to four decimal places as needed.)*
**b.** If 446 candies are randomly selected, find the probability that their mean weight is at least 0.8539 g.
The probability that a sample of 446 candies will have a mean of 0.8539 g 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?
\(\blacktriangledown\) because the probability of getting a sample mean of 0.8539 g or greater when 446 candies are selected is
\(\blacktriangledown\) exceptionally small.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe497e54d-938c-4230-bdea-816e3954b97a%2F8f42e1f7-f567-4dcb-9fa2-ab3604ed7509%2Ffsa3k0q_processed.png&w=3840&q=75)
