The weights of a certain brand of candies are normally distrbuted with a mean we

Question

The weights of a certain brand of candies are normally distrbuted with a mean weight of 0.8556 g and a standard deviation of 0.0516g. A sample of these candies package containing 470 candies, and the package label stated that the net weight is 401.2g.(f every package has 470 candies, the mean weight of the 4012 -muat exceed T-o8sse 'for the net contents to weigh at least 401 2 g.) # 1 candy is randomly selected, find the probability that t weighs more than 0.8536 g. he probability nd Round to four decimali places as needed The prctabilily ht a sample of 470 candies will have a mean of 0.8536 g or greater is Round to four decimal places as needed Gu en tese rea/a ion I swnthat tecandy company is poiing consnes with the amount darned on the later? Scos because the protuability of getting sample mean of 0.8536 gor greater when 470 candies ane selectedexceptionally smal scorE see score see score Ouions 11.590m 180mi of 5 180min of

Explanation / Answer

A) P(X > 0.8536) = P((X - mean)/SD > (0.8536 - 0.8556)/0.0516)

= P(Z > -0.04)

= 1 - P(Z < -0.04)

= 1 - 0.4840 = 0.516

B) P(X > 0.8536) = P((X - mean)/(SD/sqrt(n) > (0.8536 - 0.8556)/(0.0516/sqrt(470))

= P(Z > -0.84)

= 1 - P(Z < -0.84)

= 1 - 0.2005 = 0.7995

C) Yes because the the probability of getting a sample mean of 0.8536 or greater when 470 candies are selected 0.7995 exceptionally small.

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