The average weight of a chicken egg is 2.25 ounces with a standard deviation of 0.2 ounces. you take a random sample of a dozen eggs. what is the probability that the mean weight of the eggs in the sample will be less than 2.2 ounces?

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".  

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

And let represent the sample mean, the distribution for the sample mean is given by:

On this case  

Solution to the problem

We want this probability:

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

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

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step-by-step explanation: