Answer to Question #305952 in Statistics and Probability for Yoshy

Question

Find the probabilities of the following.

1. P(Z > 1.36)

2. P(Z < 2.45)

3. P(1.2 <z<1.4)

4. P(-2.75 << -0.56)

5. P(Z > -1.05)

Answer 1

1. P(Z > 1.36)

P(Z > 1.36)=1-P(Z<1.36)

From the Z normal distribution table,

P(Z<1.36) = 0.9131

Therefore;

P(Z > 1.36)=1-P(Z≤1.36)

= 1 - 0.9131

= 0.0869

2. P(Z < 2.45)

From the Z normal distribution table,

P(Z<2.45) = 0.9929

3. P(1.2 <z<1.4)

P(1.2 <Z<1.4) = P(Z<1.4) - P(Z<1.2)

From the Z normal distribution table,

P(Z<1.4) = 0.9192 and

P(Z<1.2) = 0.8849

Therefore;

P(1.2 <Z<1.4) = P(Z<1.4) - P(Z<1.2)

= 0.9192 - 0.8849

=0.0343

4. P(-2.75 <Z< -0.56)

P(-2.75<Z<-0.56) = P(Z<-0.56) - P(Z<-2.75)

From the Z normal distribution table,

P(Z<-0.56) = 0.28774 and

P(Z<-2.75) = 0.00298

Therefore;

P(-2.75 <Z<-0.56) = P(Z<-0.56) - P(Z<-2.75)

= 0.28774 - 0.00298

=0.2848

5. P(Z > -1.05)

P(Z > -1.05) = 1 - P(Z<-1.05)

From the Z normal distribution table,

P(Z<-1.05) = 0.1469

Therefore

P(Z > -1.05) = 1 - 0.1469

= 0.8531