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Tue 16 Sep, 2014 05:09 am
A canning industry uses tins with weight equal to 20 grams. The tin is placed on a scale and filled with red peppers until the scale shows the weight W. Then, the tin contains Y grams of peppers. If the scale is subject to a random error X~N(0, sigma = 10),
a) How is Y related to X and W?
b) What is the probability distribution of the random variable Y?
c) Calculate the value W such that 98% of the tins contain at least 400 grams of peppers.
d) Repeat the exercise assuming the weight of the tins to be a normal random variable M~N(20, sigma=5)
My attempt:
a) Y = W-20 +- X
b) Normal
c) no idea
d) no idea
@expeditor,
c) 98% of the tins will fall within +- 3SD. The problem asks for W so that "at least" 98% of the cans contain 400 gms of peppers so you only want the + side of that equation. W=400gms of peppers + 20gms for the can + 30 gms for the upside of the error band (3SDs) = 450 gms.
d) don't add 20 for the can and use sigma = 5 as above.
@expeditor,
a) Y = W - 20
b) Normal
c)
Look up the z score for 98% cumulative distribution. It is 2.05, so 2.05 sigmas = 20.5 grams. W = 400 + 20 (for the tin) + 20.5 (safety margin for 98%) = 440.5 gm
d) The sigma for the scale error and the tin error is the square root of the sum of the squares so sqrt(20^2 + 10^2) = 22.4 gm. Repeat the exercise in (c) using this sigma.
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