Questions: Find the area under the standard normal curve that lies between the following z-values. Round the answers to four decimal places. Part 1 of 2 (a) Find the area under the standard normal curve that lies between z=-2.49 and z=-0.42. The area between z=-2.49 and z=-0.42 is .3309 Part 2 of 2 (b) Find the area under the standard normal curve that lies between z=-2.27 and z=0.36. The area between z=-2.27 and z=0.36 is .

Solution Steps

To find the area under the standard normal curve between the z-values \( z = -2.49 \) and \( z = -0.42 \), we use the cumulative distribution function \( \Phi \):

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(-0.42) - \Phi(-2.49) \]

From the calculations, we find:

\[ P = 0.3309 \]

Thus, the area between \( z = -2.49 \) and \( z = -0.42 \) is \( 0.3309 \).

Next, we calculate the area under the standard normal curve between the z-values \( z = -2.27 \) and \( z = 0.36 \):

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(0.36) - \Phi(-2.27) \]

From the calculations, we find:

\[ P = 0.629 \]

Thus, the area between \( z = -2.27 \) and \( z = 0.36 \) is \( 0.629 \).

Final Answer