A random sample of size 16 is to be taken from a normal population having mean of 100 andvariance 4. What is the 90th percentile of the distribution of x?

The 90th percentile of the distribution of x is 100.64.

Given that,

Here we have

Now we requried z-score that has 0.90 area to its left. z-score 1.28 has 0.90 area to its left.

So required 90th percentile is

Learn more about the population here: link

Given:

To find:

distribution

Solution:

We require a z-score with such a 0.90 area to its left in this case. The area to the left of the z-score 1.28 is 0.90. As a consequence, the required 90th percentile is

Using formula:

Therefore, the answer is "100.64".

Learn more about the distribution here:

link