Question 281545: The problem is: The mean contents of bottles of a certain brand of soft drink is 310 ml. with a standard deviation of 5 ml.
a) What percentage of bottles would contain betwen 300 and 310 ml of contents?
b) What percentage of bottles would contain at least 304 ml of contents?
c) What is the probability of a bottle containing less than 300 ml of content?
Answer by Mathematicians(84)   (Show Source):
You can put this solution on YOUR website! Unfortunately I do not have a Z table, not to mention different Z tables calculate things differently. with me and it has been ages since I took statistics, but this should be the correct way to solve this problem.
You have the formula:
 Where X is the data, M is the mean, and S is the standard deviation. Z is the Z score it corresponds with.
a) our data is 300 and 310 and we want it in between. Well, we know 310 is the mean so that is when z = 0. We do not need to check this, we need to check 300.
Depending on your Z table, Z = -2 should correspond with some decimal. That is your answer.
b) with this one, you want to calculate z > 304. Once again, depending how your Z table looks at it, you will either have to do 1 - P(x=304) or .5 + p(x = 304)
We can begin calculating Z:
I can't really tell you how your Z table calculates probability because I have had two different Z tables in a couple different classes a few years ago.
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