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

Determine the total area under the standard normal curve for
parts (a) through (c) below. For each, be sure to draw a
standard normal curve and shade the area that is to be found.
Click here to view the standard normal distribution table (page
1).
LOADING...
Click here to view the standard normal distribution table (page
2).
LOADING...
(a) Determine the total area under the standard normal curve to
the left of
zequals=negative 2−2
or to the right of
zequals=22....

Determine the area under the standard normal curve that lies
between (a) Upper Z equals negative 0.85 and Upper Z equals 0.85,
(b) Upper Z equals negative 0.99 and Upper Z equals 0, and (c)
Upper Z equals negative 0.57 and Upper Z equals negative 0.46.
(a) Find the area under the normal curve to the left of
z = -3−3
plus the area under the normal curve to the right of
z = 3
The combined are =

Using the standard normal distribution determine:
a) The area under the curve to the left of z=-2.38
b) The area under the curve to the right of z=1.17
c) The area under the curve between z=-1.52 and z=2.04

Determine the area under the standard normal curve that lies to
the right of (a) Z = 1.52, (b) Z = 0.34, (c) Z= -0.71, and (d) Z
= -1.87 .

Determine the area under the standard normal curve that lies to
the right of
left parenthesis a right parenthesis z equals 1.66 comma(a)
z=1.66,
(b)
z equals negative 1.26 commaz=−1.26,
(c)
z equals 1.93 commaz=1.93,
and (d) z equals negative 1.37 .z=−1.37.

2. a) Find the area under the standard normal curve to the right
of z = 1.5.
b) Find the area under the standard normal curve to the left of
z = 1.
c) Find the area under the standard normal curve to the left of
z = -1.25.
d) Find the area under the standard normal curve between z = -1
and z = 2.
e) Find the area under the standard normal curve between z =
-1.5 and...

Determine the area under the standard normal curve that lies
between left parenthesis a right parenthesis Z equals negative 0.77
and Z equals 0.77, (b) Z equals negative 2.34 and Z equals 0,
and (c) Z equals negative 1.57 and Z equals 0.62.

Determine the area under the standard normal curve that lies
between left parenthesis a right parenthesis Upper Z equals
negative 0.43 and Upper Z equals 0.43, (b) Upper Z equals
negative 2.34 and Upper Z equals 0, and (c) Upper Z equals
negative 1.35 and Upper Z equals negative 0.88. LOADING... Click
the icon to view a table of areas under the normal curve.

Determine the area under the standard normal curve that lies to
the left of (a) Upper Z equals negative 0.97 comma (b) Upper Z
equals 0.71 , (c) Upper Z equals negative 1.22 , and (d) Upper
Z equals 0.66 .

Determine the area under the standard normal curve that lies to
the left of (a) Upper Z equals negative 0.36 comma (b) Upper Z
equals negative 1.29, (c) Upper Z equals negative 1.02, and (d)
Upper Z equals 0.91.

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