6. The ACME We Weigh Big Stuff company manufactures a scale for big stuff. Their
ID: 3220063 • Letter: 6
Question
6. The ACME We Weigh Big Stuff company manufactures a scale for big stuff. Their scale has quite a lot of variability to it in that when you try to weigh big stuff, the reported weight has a standard deviation of 300 pounds. Suppose the mean weight of things you use this scale for is 2400 pounds. a. Find the coefficient of variation for this scale and interpret it. b. A laboratory scale that has a standard deviation of 0.008 pounds is used to weigh items that are small. If the mean weight of items weighed using this scale is 0.015 pounds, then relative to the weight of the things this scale is used to weigh, does it make bigger errors on average than the ACME big stuff scale? Explain.Explanation / Answer
(13)
mean = 17.25
std. dev. = 2
(a)
z = (xbar - mu)/sigma
xbar = mean + z*sigma = 17.25 + 1.5*2 = 20.25
hence Bernie wieghs 20.25 pounds
(b)
1.5 is the value on standard z-scale. There is no unit for this.
(c)
P(z>1.5) = 0.0668
Hence 6.68% is the percentage of 6 months old American babies that weigh more than Bernie
(d)
P(15 < X < 18) = P((15/17.25)/2 < z < (18/17.25)/2) = P(0.4348 < z < 0.5217) = 0.5159
(e)
Find z-value for baby from Sweden
z = (13 - 18.2)/2.2 = -2.36364
lets find the weight of the baby for same z value for an american baby
xbar = 17.25 - 2.3636 * 2 = 12.5228
12.52 pounds will be the weight of the American baby.
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