Question

hw 02 ch 5: problem 4
(2 points)
the area under the standard - normal curve between z = - 0.15 and a number z_ery that is less than z = - 0.15 is approximately equal to one - fourth of the total area under the entire curve. what is the value of z_ery?

Explanation:

Step1: Recall total area under curve

The total area under the standard - normal curve is 1. One - fourth of the total area is 0.25.

Step2: Use z - table property

We know that the area to the left of \(z=- 0.15\) from the standard - normal table is \(A_1=\Phi(-0.15)\approx0.4404\). Let the \(z\) - value we want to find be \(z_{Ery}\). We want the area between \(z =-0.15\) and \(z = z_{Ery}\) such that the area to the left of \(z_{Ery}\) is \(A_1 - 0.25\). So the area to the left of \(z_{Ery}\) is \(0.4404-0.25 = 0.1904\).

Step3: Look up in z - table

Looking up the value 0.1904 in the standard - normal table (the \(z\) - table), we find that \(z_{Ery}\approx - 0.88\).

Answer:

\(z_{Ery}\approx - 0.88\)