SOLUTION: A popular soft drink is sold in 2.5-litre (i.e., 2,500 millilitres) bottles. Due to variations in the production process, bottles have a mean of 2,500 millilitres and a standard

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Question 1202307: A popular soft drink is sold in 2.5-litre (i.e., 2,500 millilitres) bottles. Due to variations in
the production process, bottles have a mean of 2,500 millilitres and a standard deviation of
22, normally distributed.
(a) If the process fills bottles by more than 25 millilitres, the overflow will cause the machine
to overflow. What is the probability of this occurring?
(b) What is the probability of underfilling bottles by at least 15 millilitres?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 2500.
standard deviation is 22.

(a) If the process fills bottles by more than 25 millilitres, the overflow will cause the machine
to overflow. What is the probability of this occurring?

i think what the probllem is saying is that the overflow will occur when the bottle is filled to more than 2525 millilitres.
that would be 25 millilitres more than the mean of 2500.
the z-score woulld be equal to (2525 - 2500) / 22 = 25 / 22 = 1.136363636.
the probability of that occurring would be equal to .1279022539.
that's the areaa to the right of that z-score.
that means that the probability of getting a z-score greater than that is 1.126363636.

(b) What is the probability of underfilling bottles by at least 15 millilitres?

the z-score would be equal to (2485 - 2500) / 22 = -15 / 22 = -.6818181818.
the probbility of that occurring would be equal to .2476768904.
that's the area to the left of that z-score.
that means that the probability of getting a z-score less than that is .2476768904.

the calculator at < rel=nofollow HREF= "https://www.hackmath.net/en/calculator/normal-distribution" target = "_blank">https://www.hackmath.net/en/calculator/normal-distribution can be used to verify these results.

here are the results from this calculator.





the calculator can be used with z-scores or raw scores.
if z-scores, the mean is 0 and the standard deviation is 1.
otherwise, use the mean and standard deviation given.