Under usual conditions, a distillation unit in a refinery can process a mean of
ID: 3023176 • Letter: U
Question
Under usual conditions, a distillation unit in a refinery can process a mean of 135,000 barrels per day of crude petroleum, with a standard deviation of 6,000 barrels per day. You may assume a normal distribution. a. Find the probability that more than 135,000 barrels will be produced on a given day. b. Find the probability that more than 130,000 barrels will be produced on a give day. c. Find the probability that more than 150,000 barrels will be produced on a given day. d. Find the probability that less than 125,000 barrels will be produced on a given day. e. Find the probability that less than 100,000 barrels will be produced on a given day.Explanation / Answer
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 135000
u = mean = 135000
s = standard deviation = 6000
Thus,
z = (x - u) / s = 0
Thus, using a table/technology, the right tailed area of this is
P(z > 0 ) = 0.5 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 130000
u = mean = 135000
s = standard deviation = 6000
Thus,
z = (x - u) / s = -0.833333333
Thus, using a table/technology, the right tailed area of this is
P(z > -0.833333333 ) = 0.797671619 [ANSWER]
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c)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 150000
u = mean = 135000
s = standard deviation = 6000
Thus,
z = (x - u) / s = 2.5
Thus, using a table/technology, the right tailed area of this is
P(z > 2.5 ) = 0.006209665 [ANSWER]
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d)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 125000
u = mean = 135000
s = standard deviation = 6000
Thus,
z = (x - u) / s = -1.666666667
Thus, using a table/technology, the left tailed area of this is
P(z < -1.666666667 ) = 0.047790352 [ANSWER]
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e)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 100000
u = mean = 135000
s = standard deviation = 6000
Thus,
z = (x - u) / s = -5.833333333
Thus, using a table/technology, the left tailed area of this is
P(z < -5.833333333 ) = 2.71654*10^-9 [ANSWER]
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