Question

find the area under the standard normal curve between z = 1.5 and z = 2.5.
a. 0.9332
b. 0.9938
c. 0.0606
d. 0.9816

Explanation:

Step1: Use z - table values

We know that the area under the standard - normal curve to the left of \(z = z_1\) is given by \(\varPhi(z_1)\). The area under the standard - normal curve between \(z = 1.5\) and \(z = 2.5\) is \(\varPhi(2.5)-\varPhi(1.5)\).
From the standard normal table, \(\varPhi(2.5)=0.9938\) and \(\varPhi(1.5)=0.9332\).

Step2: Calculate the difference

\[

$$\begin{align*} \text{Area}&=\varPhi(2.5)-\varPhi(1.5)\\ &=0.9938 - 0.9332\\ &=0.0606 \end{align*}$$

\]

Answer:

C. 0.0606