Question

Determine the total area under the standard normal curve in parts (a) through (c) below.

a- Find the area under the normal curve to the left of z = -3 plus the area under the normal curve to the right of z = 3

the combined area under the normal curve to the right of z = 3_____

(b) Find the area under the normal curve to the left of z equals=−1.52

plus the area under the normal curve to the right of z equals=2.52

the combined area is

(c) Find the area under the normal curve to the left of z equals=−0.22 plus the area under the normal curve to the right of

z equals=1.10

The combined area is____

Answer 1

Note: Z~N(0,1)

So, = derived from standard normal table or R studio codes are given below.

Combined areas are given below

a)

P(Z<-3) + P(Z>3) = 0.0013+0.0013 = 0.0026

b)

P(Z<-1.52) +P(Z>2.52) = 0.0643+0.0059 = 0.0702

c)

P(Z<-0.22) + P(Z>1.1) = 0.4129+0.1357 = 0.5486

R Codes:

> 1-pnorm(3)
[1] 0.001349898
> pnorm(-3)
[1] 0.001349898

> pnorm(-1.52)
[1] 0.06425549
> 1-pnorm(2.52)
[1] 0.005867742
> pnorm(-0.22)
[1] 0.4129356
> 1-pnorm(1.1)
[1] 0.1356661