Question

Find the z-value so that the area to the right of z (shaded in the picture) is 0.0139.

Answer 1

To answer this question, we need to make use of the cumulative standard normal distribution. No matter what the probability we are finding for. The cumulative normal distribution will give us a z-score (the value in standard deviations the raw value, x, is from the mean).

Then, we have that the z-score is given by:

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

We have that the cumulative standard normal distribution gives us value for values less than a z-score. Then, we need to find this z-score using the cumulative standard distribution as follows:

$P(xThen, finding the value that corresponds to this probability in a cumulative standard distribution using a table, we have that z = 2.2.

Therefore:

[tex]P(z<2.2)=0.9861$

Or

$P(z>2.2)=0.0139$

In summary, the value for z is equal to z = 2.2.