SOLUTION: The fill amount of soft drink bottles is normally distributed with a mean of 2.0 litres and a standard deviation of 0.07 litres. If you select a random sample of 25 bottles, what i

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Question 1203068: The fill amount of soft drink bottles is normally distributed with a mean of 2.0 litres and a standard deviation of 0.07 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 90% that the sample mean will contain at least how much soft drink?
e. The probability is 90​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
population mean is 2.0
population standard deviation is .07
sample size is 25.

standard error = standard deviation / square root of sample size = .07 / sqrt(25) = .07 / 5 = .014.

x = sample mean

a. what is probbility that x is Between 1.99 and 2.0 litres?

probability is equal to .2625

b. what is probability that x is Below 1.98 litres?

probability is equal to .0766

c. what is probability that x is Above 2.01 litres?

probability is equal to .2375

d. The probability is 90% that the sample mean will contain at least how much soft drink?

the proabability is 90% that the mean of the sample will be greater than or equal to 1.9821 liters of soft drink.


e. The probability is 90​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)?

the probability is 90% that the sample mean will be between 1.97697 and 2.02303 liters.

here's what the answers look like on a graph.