Question 202628: Reposting again with proper data - Thanks...
In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler sets the filling machine so the mean is 2.02 liters and a standard deviation of 0.05 liters. Under these circumstances, please answer below.
a. Between 1.90 and 2.0 liters
b. Between 1.90 and 2.10 liters
1) 0.5464
c. Below 1.90 liters or above 2.10 liters
1)
d. 99% of the bottles contain at least how much soft drink?
e. 99% of the bottles contain an amount that is between which two values (symmetrically distributed) around the mean
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler sets the filling machine so the mean is 2.02 liters and a standard deviation of 0.05 liters. Under these circumstances, please answer below.
a. P(Between 1.90 and 2.0 liters)
Find the z-values for 1.9 and 2
z(1.9) = (1.9-2.02)/0.05 = -2.4
z(2) = (2-2.02)/0.05 = -0.4
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P(1.9 < x < 2) = P(-2.4 < z < -0.4) = 0.3364
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b. Between 1.90 and 2.10 liters
Use the same procedure as in part "a" to get
P(1.9 < x < 2.1) = 0.9370
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c. Below 1.90 liters or above 2.10 liters
Use the results of part "b" to get:
P(x < 1.9 or x > 2.1) = 1 - 0.9370 = 0.0630
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d. 99% of the bottles contain at least how much soft drink?
Find the z-value of 0.99 by using InVNorm(0.99) = 2.3263
Find the corresponding "x" value using x = z*sigma + u
x = 2.3263*0.05 + 2.02 = 2.1363 liters
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e. 99% of the bottles contain an amount that is between which two values (symmetrically distributed) around the mean
Comment: If 99% is distributed around the mean, each tail
has 0.005 or 0.5%
Find the z-value of 0.005 and use x = z*sigma + u to find the x-values.
InVNorm(0.005) = -2.5758
x = -2.5758*0.05+2.02 = 1.8912 liters
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InVNorm(.995) = =2.5758
x = 2.5758*0.05+2.02 = 2.1488 liters
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Cheers,
Stan H.
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