Question 998690: Suppose the weights of packages of Oreo cookies have a normal distribution with a mean of 252 grams and a standard deviation of 9 grams.
(a) What proportion of all packages weigh between 245 grams and 265grams? (b) What proportion of all packages weigh more than 260 grams?
(c) What weight should be advertised on the packages so that only 10% of packages fall below the advertised weight?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! mean=252 gm
sd=9 gm
between 245 and 265 is
z=(245-252)/9 = -0.778
z=(265-252)/9=13/9=1.444
Probability z is between those two values is 0.7073. This makes sense, as it is about +/- 1 sd
greater than 260 gm, z=(260-252)/9=8/9=0.8888
probability z> than 0.8888=0.1871
Only 10% of packages fall below the advertised weight of x gm. That is impossible as the sentence is written.Half fall below the advertised weight, UNLESS one assumes that the package weight is 252 gm regardless. Then the lower 10% ile is 1.28*9=11.52 gm. away from the mean. If that is subtracted from 252 gm, then 240.48 gm would be advertised, and then 10% would fall below the mean weight of 252 gm and sd of 9 gm.
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