SOLUTION: The fill amount of soft drink bottles is normally distributed with a mean of 2.0 litres and a standard deviation of 0.05 litres. If you select a random sample of 25 bottles, what i

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Question 785428: The fill amount of soft drink bottles is normally distributed with a mean of 2.0 litres and a standard deviation of 0.05 litres. If you select a random sample of 25 bottles, what is the probability that the sample mean will be�
a. Between 1.99 and 2.0 litres?
b. Below 1.98 litres?
c. Above 2.01 litres?
d. The probability is 99% that the sample mean will contain at least how much soft drink?

Answer by stanbon(75887) (Show Source):
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The fill amount of soft drink bottles is normally distributed with a mean of 2.0 litres and a standard deviation of 0.05 litres. If you select a random sample of 25 bottles, what is the probability that the sample mean will be�
a. Between 1.99 and 2.0 litres?
z(1.99) = (1.99-2)/[0.05/sqrt(25)] = -
z(2) = 0
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P(1.99 < x-bar < 2.0) = P(-1 < z < 0) = 0.3413
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b. Below 1.98 litres?
c. Above 2.01 litres?
Note: For "b" and for "c"
Find the z-values
Find the x-bar values
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d. The probability is 99% that the sample mean will contain at least how much soft drink?
Find the z-values framing 99% around the mean.
+-invNorm(0.005) = +-2.5758
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Lower limit:: x-bar = -2.5758*(0.05/5)+2 = 1.9742
Upper limit:: x-bar = +2.5758*(0.05/5)+2 = 2.0258
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Cheers,
Stan H.
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