Question

Find the area under the standard normal curve between:

(a) P(-1.5<z<1.25)

(b) to the right of z=1.06

P(z<-2.58 or z>2.58)

Answer #1

Note: Z~N(0,1)

So, P(Z<z) or P(Z<=z) is th cdf of standard normal, it can be derived from R studio : code : pnorm(z) or standard normal table

a) P(-1.5< z< 1.25) = P(Z<1.25) - P(Z<-1.5) = 0.8943502 - 0.0668072 = 0.827543

b) P(Z>1.06) = 1-P(Z<=1.06) =1- 0.8554277 = 0.1445723

c) P(Z<-2.58 or Z>2.58) = P(Z<-2.58) +P( Z>2.58) = P(Z<-2.58) +1-P( Z<2.58) = 0.00494 +(1- 0.9956) = 0.00988

**R Codes:**

**> pnorm(1.25)
[1] 0.8943502**

**pnorm(-1.5)
[1] 0.0668072
> pnorm(1.06)
[1] 0.8554277
> pnorm(-2.58)
[1] 0.004940016
> pnorm(2.58)
[1] 0.99506**

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...

find the area under the standard normal curve to the right z=
1
find the area under the standard normal curve to the left z=
1.25
find the value z(alfa) z0.04

a)Find the area under the standard normal curve between
z = -1.86 and z = 1.1, P(-1.86 <
z < 1.1). (Give your answer correct to four decimal
places.)
b)Find the area under the standard normal curve between
z = -2.53 and z = 1.4, P(-2.53 <
z < 1.4). (Give your answer correct to four decimal
places.)
c)Consider the normal curve. (Give your answers correct to four
decimal places.)
1) Find the area to the right of z =...

(A) Find the area under the standard normal curve between -0.34
and 1.59:
(B) Find the area under the standard normal curve between -1.5
and 1
(C) Find the area under the standard normal curve that lies to
the left of 2.24
(d) Find the area under the standard normal curve that lies to
the left of -0.42
(e) Find the area under the standard normal curve that lies to
the right of -2.3
(f) Find the area under the...

1)
a) Find the area under the Standard Normal Curve in-between z =
-0.59 and z = 2.86
Use the Normal table and give answer using 4 decimal places.
b) Find the area under the Standard Normal Curve in-between z =
-0.36 and z = 2.63
Use the Normal table and give answer using 4 decimal places.
c) Find P(z < 1.75)
Use the Normal table and give answer using 4 decimal places.

Find the area under the standard normal curve that lies between
the following two z values. Round your answers to at least four
decimal places.
(a)Find the area under the standard normal curve that lies
between = z − 1.28 and = z 1.36 .
(b)Find the area under the standard normal curve that lies
between = z − 2.17 and = z − 1.92 .
(c)Find the area under the standard normal curve that lies
between = z 1.36...

(a)Find the area under the standard normal curve that lies
outside the interval between =z−1.73 and =z1.99.
(b)Find the area under the standard normal curve that lies
outside the interval between =z−1.75 and =z0.99.
(c)Find the area under the standard normal curve that lies
outside the interval between =z0.89 and =z1.41.
(d)Find the area under the standard normal curve that lies
outside the interval between =z−1.80 and =z−1.33.

When considering area under the standard normal curve, decide
whether the area between z=-1.5 and z= -1 is bigger than, smaller
than, or equal to the area between z=2 and z= 2.5

Find the value of z if the area under a standard normal curve
(a) to the right of z is 0.3300 (b) to the left of z is .1112, (c)
between 0 and z, with z >0, is ,4803, and (d) between -z and z,
with z > 0, is .9250.

Find the value of z if the area under a standard normal curve
(a) to the right of z is 0.3974; (b) to the left of z is 0.0918;
(c) between 0 and z, with z > 0, is 0.4783; and (d) between -z
and z, with z > 0, is 0.9412
also i think you need to use the standard normal distribution
table.

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