Question

Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean µ = 0 and standard deviation σ = 1. (12 pts.)

a. The area to the left of z is 15%.

b. The area to the right of z is 65%.

c. The area to the left of z is 10%.

d. The area to the right of z is 5%

e. The area between –z and z is 95%. (Hint: draw a picture and figure out the area to the left of the –z)

f. The area between –z and z is 99%

USING EXCEL.

Answer 1

Ans:

a)

P(Z<z)=0.15

z=normsinv(0.15)=-1.036

b)

P(Z>z)=0.65

P(Z<z)=1-0.65=0.35

z=normsinv(0.35)=-0.385

c)

P(Z<z)=0.1

z=normsinv(0.1)

z=-1.282

d)

P(Z>z)=0.05

P(Z<z)=1-0.05=0.95

z=normsinv(0.95)=1.645

e)Tails area=1-0.95=0.05

half tail area=0.05/2=0.025

z=normsinv(0.025) or normsinv(1-0.025)

z=+/-1.96

f)

Tails area=1-0.99=0.01

half tail area=0.01/2=0.005

z=normsinv(0.005) or normsinv(1-0.005)

z=+/-2.576