http://www.brewershilllifestyle.com/beer-bottling-machine/
How can i arrive to an answer with this statistics problem, please explain?
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.25ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than 12.5 ounces of beer.
i meant fewer than 12.15 ounces of beer. in that last sentence
We are given that U=true or population mean weight bottles of beer=12.25 and δ=standard deviation of weight bottles of beer=0.04 and the probability distribution of the mean amount weight of beer poured by this filling machine is normally distributed. And we are asked to find the probability that the bottle contains x<12.5 ounces of beer.
So, the probability that the bottle contains fewer than 12.5 ounces of beer
= P(x<12.5)
= P{[(x-u)/s]<[(12.5-12.25)/0.04]}
= P(z<6.25)
= P(z<0) + P(0
= 0.999
= 99.9%
Therefore, there is a 99.9% chance that the bottle contains fewer than 12.5 ounces of beer.
Hope this helps.
Small beer bottling line
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