Answer to Question #181307 in Statistics and Probability for Rustom

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