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.

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.

a

b

c

d

e

f

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  

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  

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;

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

and

So

=>  

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  

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  

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;

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

and

So

=>  

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?