A certain brand of candies have a mean weight of 0.85740.8574g and a standard de

Question

A certain brand of candies have a mean weight of 0.85740.8574g and a standard deviation of 0.05220.0522. A sample of these candies came from a package containing 448448 candies, and the package label stated that the net weight is 382.3382.3g. (If every package has 448448 candies, the mean weight of the candies must exceed StartFraction 382.3 Over 448 EndFraction382.3448equals=0.85330.8533 g for the net contents to weigh at least 382.3382.3 g.

a. If 1 candy is randomly selected, find the probability that it weighs more than 0.85330.8533

g.The probability is nothing.

(Round to four decimal places as needed.)

b. If 448448 candies are randomly selected, find the probability that their mean weight is at least 0.85330.8533

g.The probability that a sample of 448448 candies will have a mean of 0.85330.8533 g or greater is nothing.

(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?

Explanation / Answer

a) P(X>0.8533) =1-P(X<0.8533)=1-P(Z<(0.8533-0.8574)/0.0522)=1-P(Z<-0.0785)=1-0.4687=0.5313

b)for 448 candies; std error =std deviation/(n)1/2 =0.0025

hence P(X>0.8533)=1-P(Z<(0.8533-0.8574)/0.0025)=1-P(Z<-1.6625)=1-0.0482=0.9518

c) No as probabilty of having weight above described weight is more then 95%.

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