Question

Given a standard normal distribution, find the area under the curve that lies (a) to the left of z = −1.39; (b) to the right of z = 1.96; (c) between z = −2.16 and z = −0.65; (d) to the left of z = 1.43; (e) to the right of z = −0.89; (f) between z = −0.48 and z = 1.74.

Answer 1

Complete Question

Given a standard normal distribution, find the area under the curve that lies

(a) to the left of z = −1.39;

(b) to the right of z = 1.96;

(c) between z = −2.16 and z = −0.65;

(d) to the left of z = 1.43;

(e) to the right of z = −0.89;

(f) between z = −0.48 and z = 1.74.

Answer:

a

  $P(Z < -1.39) = 0.082264$

b

 $P(Z > 1.96) = 0.025$

c

 $P(-2.16 < Z < -0.65 ) =0.2457$

d

 $P(Z < 1.43) = 0.92364$

e

  $P(Z > -0.48) = 0.68439$

f

  $P(-0.48 < Z < 1.74 ) =0.6435$

Step-by-step explanation:

Considering a

From the question we are told that

   The  z-score is  z =  -1.39

Generally from the z table the  area under the curve that lies to the left of  z =  -1.39 is  

     $P(Z < -1.39) = 0.082264$

Considering b

From the question we are told that

   The  z-score is  z = 1.96

Generally from the z table the  area under the curve that lies to the right of  z = 1.96 is  

     $P(Z > 1.96) = 0.025$

Considering c

From the question we are told that

   The z-score is  z = −2.16 and z = −0.65

Generally from the z table the  area under the curve that lies between z = −2.16 and z = −0.65;

   $P(-2.16 < Z < -0.65 ) = P(Z < -0.64 ) - P( Z < -2.16)$

From the z table the area under  (Z <  -0.64 )   and  ( Z <  -2.16) is  

      $P(Z < -0.64 ) = 0.26109$

and

      $P( Z < -2.16) = 0.015386$

So

     $P(-2.16 < Z < -0.65 ) =0.26109- 0.015386$

=>  $P(-2.16 < Z < -0.65 ) =0.2457$

Considering d

From the question we are told that

   The  z-score is  z = 1.45

Generally from the z table the  area under the curve that lies to the left of z = 1.43 is  

     $P(Z < 1.43) = 0.92364$

Considering e

From the question we are told that

   The  z-score is  z = -0.48

Generally from the z table the  area under the curve that lies to the right of  z = 0.48 is  

     $P(Z > -0.48) = 0.68439$

Considering f

From the question we are told that

   The z-score is  z = −0.48  and z = 1.74

Generally from the z table the  area under the curve that lies between z = −2.16 and z = −0.65;

   $P(-0.48 < Z < 1.74 ) = P(Z < 1.74 ) - P( Z < -0.48)$

From the z table the area under  (Z <  1.74 )   and  ( Z <  -0.48) is  

      $P(Z < 1.74 ) = 0.95907$

and

      $P( Z < -0.48 ) = 0.31561$

So

     $P(-0.48 < Z < 1.74 ) = 0.95907 - 0.31561$

=>  $P(-0.48 < Z < 1.74 ) =0.6435$

Answer 2

The standard normal table shows the mathematical table which represent the value below a z-score in standard normal distribution. It is also known as z-table.

(a) The correct answer is 0.082264.

(b) The correct answer is 0.025

(c) The correct answer is 0.2457.

(d) The correct answer is 0.68439.

(e) The correct answer is 0.6435

Given:

(a)

The  z-score is  z =  -1.39

Refer the z-table area under the curve that lies to the left of $z=-1.39$,

$P(Z<-1.39)=0.082264$

(b)

.The  z-score is  z = 1.96

Refer the z-table area under the curve that lies to the right of $z=1.96$,

$P(Z>1.96)=0.025$

(c)

The  z-score is  $z = -2.16$ and $z=-0.65$

Refer the z-table area under the curve that lies between $z = -2.16$ and $z=-0.65$,

$P(-2.16<Z<-0.65)=P(Z<-0.64)-P(Z<-2.16)$

Thus,

$P(Z<-0.64)=0.26109\\P(Z<-2.16)=0.015386\\P(-2.16<Z<-0.65)=0.26109-0.015386\\P(-2.16<Z<-0.65)=0.2457$

(d)

The  z-score is  $z =1.45$

Refer the z-table area under the curve that lies to the right $z = 1.45$,

$P(Z<1.45)=0.92364$

(e)

The  z-score is  $z = -0.48$

Refer the z-table area under the curve that lies to the right $z = -0.48$,

$P(Z>-0.48)=0.68439$

(f)

The z-score is  $z =-0.48$  and $z = 1.74$

Refer the z-table area under the curve that lies between $z =-0.48$  and$z = 1.74$,

The z table the area under  $(Z < 1.74 )$ is,

$P(Z<1.74)=0.95907$

The z table the area under  $(Z < -0.48 )$ is,

$P(Z<-0.48)=0.31561$

Calculate the area under the curve that lies between $z =-0.48$  and$z = 1.74$,

$P(-0.48<Z<1.74)=P(Z<1.74)-P(Z<-0.48)\\P(-0.48<Z<1.74)=0.95907-0.31561\\P(-0.48<Z<1.74)=0.6435$

Thus,

(a) The correct answer is 0.082264.

(b) The correct answer is 0.025

(c) The correct answer is 0.2457.

(d) The correct answer is 0.68439.

(e) The correct answer is 0.6435

Learn more about z-table here:

https://brainly.com/question/24163209