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dexar [7]
3 years ago
7

Bottling cola A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 3

00 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean μ = 298ml and standard deviation σ = 3ml.
What is the probability that a randomly selected bottle contains less than 295 ml? Show your work.
Mathematics
1 answer:
erik [133]3 years ago
4 0

Answer:

P(X

And we can find this probability using the normal standard table or excel:

P(Z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the amount of ml of a population, and for this case we know the distribution for X is given by:

X \sim N(298,3)  

Where \mu=298 and \sigma=3

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard table or excel:

P(Z

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