A certain brand of candies have a mean weight of 0.8599 g & a SD of 0.0511. A sa

Question

A certain brand of candies have a mean weight of 0.8599 g & a SD of 0.0511. A sample of these candies came from a package containing 443 candies & the package label stated the net weight is 378.0 g. (If every package has 443 candies, the mean weight must exceed 378.0/443 = 0.8532 g for the net contents to weigh at least 378.0 g)
a) if 1 candy is randomly selected, find the probability that it weighs more than 0.8532 g. (Round 4 dp)
b) if 443 candies are randomly selected, find the probability that the mean is 0.8532 g or greater. (Round 4 dp)
c) given these results, does it seem that the candy company is providing customers with the amount claimed on their label? Yes or No? The probability of getting a sample mean of 0.8532 or greater when 443 are selected IS or IS NOT exceptionally small? A certain brand of candies have a mean weight of 0.8599 g & a SD of 0.0511. A sample of these candies came from a package containing 443 candies & the package label stated the net weight is 378.0 g. (If every package has 443 candies, the mean weight must exceed 378.0/443 = 0.8532 g for the net contents to weigh at least 378.0 g)
a) if 1 candy is randomly selected, find the probability that it weighs more than 0.8532 g. (Round 4 dp)
b) if 443 candies are randomly selected, find the probability that the mean is 0.8532 g or greater. (Round 4 dp)
c) given these results, does it seem that the candy company is providing customers with the amount claimed on their label? Yes or No? The probability of getting a sample mean of 0.8532 or greater when 443 are selected IS or IS NOT exceptionally small?
a) if 1 candy is randomly selected, find the probability that it weighs more than 0.8532 g. (Round 4 dp)
b) if 443 candies are randomly selected, find the probability that the mean is 0.8532 g or greater. (Round 4 dp)
c) given these results, does it seem that the candy company is providing customers with the amount claimed on their label? Yes or No? The probability of getting a sample mean of 0.8532 or greater when 443 are selected IS or IS NOT exceptionally small?

Explanation / Answer

a) this is a normal distirbution.

x: weight of candies

P(x>0.8532)=0.5522

use NORMDIST function in excel and subtract with 1.

b) sd=0.0511/sqrt(443)=0.002428

P(x>0.8532)=0.9971

c) the above probability is large. Hence the candy company is providing customers with the amount claimed in their label.

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