Question

find the probabilities for each using the standard normal distribution. p(0<z<0.95), p(0<z<1.96), p(-1.38<z<0), p(z>2.33), p(z<-1.51), p(1.56<z<2.13), p(z<1.42)

Answer 1

Refer to the following Standard normal table :

1) P(0<Z<0.95) = P(Z<0.95) - P(Z<0)

Using the table above,

To find this probability, P(Z<0.95) , we look the value corresponding to 0.9 in the row and 0.05 in the column

P(Z<0.95) = 0.8289

To find this probability, P(Z<0) , we look the value corresponding to 0.0 in the row and 0.00 in the column  

P(Z<0) = 0.5

P(0<Z<0.95) = P(Z<0.95) - P(Z<0) = 0.8289 - 0.5 = 0.3289

Similarly, we can find all the probabilities

2)

P(0<Z<1.96) = P(Z<1.96) - P(Z<0)

Using the table above,

To find this probability, P(Z<1.96) , we look the value corresponding to 1.9 in the row and 0.06 in the column

P(Z<1.96) = 0.9750

P(0<Z<1.96) = P(Z<1.96) - P(Z<0) = 0.9750 - 0.50 = 0.475

3)

P(-1.38<Z<0) = P(Z<0) - P(Z<-1.38) = P(Z<0) - ( 1 - P(Z<1.38) ) = P(Z<1.38) + P(Z<0) - 1

Using the table above,

To find this probability, P(Z<1.38) , we look the value corresponding to 1.3 in the row and 0.08 in the column

P(Z<1.38) = 0.9162

P(-1.38<Z<0) = P(Z<1.38) + P(Z<0) - 1 = 0.9162 + 0.5 - 1 = 0.4162

4)

P(Z>2.33) = 1 - P(Z<2.33)

Using the table above,

To find this probability, P(Z<2.33) , we look the value corresponding to 2.3 in the row and 0.03 in the column

P(Z<2.33) = 0.9901

P(Z>2.33) = 1 - P(Z<2.33) = 1 - 0.9901 = 0.0099

5)

P(Z<-1.51) = 1 - P(Z<1.51)

Using the table above,

To find this probability, P(Z<1.51) , we look the value corresponding to 1.5 in the row and 0.01 in the column

P(Z<1.51) = 0.9345

P(Z<-1.51) = 1 - P(Z<1.51) = 1 - 0.9345 = 0.0655

6)

P(1.56<Z<2.13) = P(Z<2.13) - P(Z<1.56)

Using the table above,

To find this probability, P(Z<1.56) , we look the value corresponding to 1.5 in the row and 0.06 in the column

P(Z<1.56) = 0.9406

To find this probability, P(Z<2.13) , we look the value corresponding to 2.1 in the row and 0.03 in the column

P(Z<2.13) = 0.9834

P(1.56<Z<2.13) = P(Z<2.13) - P(Z<1.56) = 0.9834 - 0.9406 = 0.0428

7)

Using the table above,

To find this probability, P(Z<1.42) , we look the value corresponding to 1.4 in the row and 0.02 in the column

P(Z<1.42) = 0.9222