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.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
![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)
