Question

Find the area under the normal curve in each of the following cases. First Draw the normal curve then label it.

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

1. P(Z>1.63) = 1 - P(Z<1.63)

= 1 - 0.9484

= 0.0516

2. P(-1.36<Z<2.55) = P(Z<2.55) -P(Z < -1.36)

= 0.9946 - 0.0869

= 0.9077

3. P(Z< -1.78) = 0.0375

4. P(-2.76<Z< -1.25) = P(Z< -1.25) - P(Z < -2.76)

= 0.1056 - 0.0028

= 0.1028

5. P(1.56<Z<2.51) = P(Z<2.51) - P(Z<1.56)

= 0.9939 - 0.9406

= 0.0533