Answer the following questions a What is the area under the

Answer the following questions

a. What is the area under the standard normal curve to the right of z - .97?

b. What is the area under the standard normal curve to the left of z = 2.91?

c. What is the area under the standard normal curve between z = 2.53 and z = 3.09?

d. What is the area under the standard normal curve between z = -2.14 and z = -1.95?

e. What is the area under the standard normal curve to the left of z = -2.84?

f. What is the area under the standard normal curve to the right of z = -1.74?

g. If z is the standard normal variable, find P (-2.19 < z < 2.14)

h. If z is the standard normal variable, find P (z < -1.21)

Solution

a) To find the area under the standard normal curve to the right of z= 0.97

To find the area under the standard normal curve to the right of z= 0.97,First find the area between z=0 and z=0.97.Then subtract this area from 0.5 which is the total area to the right z=0.Using the standard normal distribution table,area between z=0 and z=0.97 is 0.334.Consequently the required area is 0.5-0.334=0.166.

b) To find the area under the standard normal curve to the left of z = 2.91.

Using the standard normal distribution table,area between z=0 and z=2.91 is 0.9982.

c) To find the area under the standard normal curve between z = 2.53 and z = 3.09

Using the standard normal distribution table,area between z=2.53 and z=3.09 ,The area between z=0 and z=2.53 is 0.9943.area between z=0 and z=3.09 is 0.9990.

The area under the standard normal curve between z = 2.53 and z = 3.09=0.9990-0.9943=0.0047.

d) To find the area under the standard normal curve between z = -2.14 and z = -1.95.

Using the standard normal distribution table,area between z=-2.14 and z=-1.95 ,The area between z=0 and z=-2.14 is 0.0162.area between z=0 and z=-1.95 is 0.0256.

The area under the standard normal curve between z = -2.14 and z = -1.95=0.0256-0.0162=0.0094.

e) To find the area under the standard normal curve to the left of z = -2.84.

Using the standard normal distribution table,area between z=0 and z=-2.84 is 0.0023.

f) To find the area under the standard normal curve to the right of z = -1.74

Using the standard normal distribution table,area between z=0 and z=-1.74 is 0.0409. the area under the standard normal curve to the right of z = -1.74 is 1-0.0409=0,9591.

g) Find z is the standard normal variable, find P (-2.19 < z < 2.14)
Using standard normal distribution table.

P (-2.19 < z < 2.14) =P(z<2.14)-P(z<-2.19)=0.9838-0.0143=0.9695.

h) z is the standard normal variable, find P (z < -1.21)

Using standard normal distribution table.

P (z < -1.21)=0.1131.