# Statistics Help

• Oct 29th 2007, 03:20 PM
Amy
Statistics Help
Soda bottles are filled to 2.0 liters with a standard deviation of 0.05 liters and are normally distributed. 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 liters
.
b The probability is 99% that the sample mean will contain at least how much soft drink?

c. The probability is 99% that the sample mean will contain an amount that is between which two values (symmetrically distributed around the mean)?

For the first one I got the ans 0.0793
The last two I didn't understand, the questions.
• Oct 30th 2007, 12:37 AM
CaptainBlack
Quote:

Originally Posted by Amy
Soda bottles are filled to 2.0 liters with a standard deviation of 0.05 liters and are normally distributed. 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 liters

The standard deviation of the mean of a sample of size 25 will be:

sigma=0.05/sqrt(25)=0.01.

A fill of between 1.99 and 2.0, is from z-score -1, to 0, and:

p(-1<z<0)= 0.3413

RonL
• Oct 30th 2007, 12:43 AM
CaptainBlack
Quote:

Originally Posted by Amy
Soda bottles are filled to 2.0 liters with a standard deviation of 0.05 liters and are normally distributed. If you select a random sample of 25 bottles what is the probability that the sample mean will be:

b The probability is 99% that the sample mean will contain at least how much soft drink?

The z-score x such that p(z<x)=0.01 is ~-2.33, so the fill that will give us
this z-score is y:

-2.33 = (y-2.0)/0.01, or y~=1.9977 litres

RonL