Question

Find the area under the normal curve in each of the following cases.

1. to the right of𝑧 = 1.63

2. between 𝑧 = −1.36 and 𝑧 = 2.55

3. to the left of𝑧 = −1.78

4. between 𝑧 = −2.76 and 𝑧 = −1.25

5. between 𝑧 = 1.56 and 𝑧 = 2.51

Answer 1

To find the area under the normal curve we need to use CDF of standard normal random value $\Phi(x)$

1. To the right of 𝑧 = 1.63: $Pr(X > z) = 0.0516$

2. between 𝑧 = −1.36 and 𝑧 = 2.55: $Pr(z_1 < X < z_2) = 0.9077$

3. to the left of𝑧 = −1.78: $Pr(X < z) = 0.0375$

4. between 𝑧 = −2.76 and 𝑧 = −1.25: $Pr(z_1 < X < z_2) = 0.1028$

5. between 𝑧 = 1.56 and 𝑧 = 2.51: $Pr(z_1 < X < z_2) = 0.0533$