Question 718355: 5. A Petroleum Company fills steel drums with a lubricating oil. The mechanism that fills the drums, set equal to the mean that wants to be achieved, is not very precise and sometimes it underfills the drums and sometimes it overfills them in such a way that the weight of the oil in the drum is normally distributed with mean 250 pounds and standard deviation 2 pounds. The company doe not want to underfill the drums so it conducts routine testing on the weight of the drums. A drum is under filled if its weight is below 248 pounds.
a. What proportion of all drums are underfilled?
b. If a random sample of 20 drums, what is the probability that 4 drums are underfilled?
c. If a random sample of 90 drums is selected, what is average number of drums you expect to observe underfilled?
d. What should the valve setting be to ensure that less than 1 percent of all drums are underfilled?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A Petroleum Company fills steel drums with a lubricating oil. The mechanism that fills the drums, set equal to the mean that wants to be achieved, is not very precise and sometimes it underfills the drums and sometimes it overfills them in such a way that the weight of the oil in the drum is normally distributed with mean 250 pounds and standard deviation 2 pounds. The company doe not want to underfill the drums so it conducts routine testing on the weight of the drums. A drum is under filled if its weight is below 248 pounds.
a. What proportion of all drums are underfilled?
z(248) = (248-250)/2 = -1
P(x < 248) = P(z < -1) = normalcdf(-100,-1) = 0.1587
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b. If a random sample of 20 drums, what is the probability that 4 drums are underfilled
Binomial Problem with n = 20 ; p(under) = 0.1587
P(x = 4) = 20C4(0.1587)^4(0.8413)^16 = binompdf(20,0.1587,4) = 0.1936
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c. If a random sample of 90 drums is selected, what is average number of drums you expect to observe underfilled?
average = mean = np = 90*0.1936 = 14.283
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d. What should the valve setting be to ensure that less than 1 percent of all drums are underfilled?
Find the z-value with a left tail of 1%:
invNorm(0.01) = -2.3263*2+250 = 245.347
Find the corresponding x-value using
x = z*s+u
x = -2.3263*2+250 = 245.237
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Cheers,
Stan H.
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