The heights of baby giraffe are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 baby giraffes are randomly selected, find the probability that they have a mean height less than 63.0 inches.

And we can solve this using the following z score formula:

And if we use this formula we got:

So we can find this probability equivalently like this:

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 heights of a population, and for this case we know the distribution for X is given by:

Where and

We select n =100. Since the distribution for X is normal then we know that the distribution for the sample mean is given by:

We want this probability:

And we can solve this using the following z score formula:

And if we use this formula we got:

So we can find this probability equivalently like this:

step-by-step explanation:

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