Question

A vitamin supplement has a mean weight of 1.558 g per tablet with a standard deviation of 0.003 g. They are sold in bottles labeled 450 tablets. The machine fills the bottles based upon weight (instead of counting). Where should the weight be set on the machine if no more than 0.8% can be below 450 tablets? What percentage of bottles have more than 452 tablets?

Answer 1

Converting the standard deviation and mean in terms of weight, we get,

Mean Weight of a bottle = 450 * 1.558 = 701.1 gms and SD = 0.003 * sqrt(450) = 0.0636

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(a) No more than 0.8% should have less than 450 tablets, i.e, P(X x) = 0.008

From the normal tables the p value at 0.008 is -2.4089

Therefore -2.4089 = (X - 701.1)/0.0636

X = 701.1 + (-2.4089*0.0636) = 700.9468 gms         700.947 gms

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(b) The weight of 452 tablets = 1.558 * 452 = 704.216

Therefore P(X > 704.216) = 1 - P(X < 704.216)

Z = (704.216 -701.1) / 0.0636 = 48.99

Therefore P(X < 704.216) = 1.000

Therefore P(X > 704.216) = 1 - 1 = 0 = 0.00%

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