Answer the following questions about the standard normal random variable z. (use 4 decimal places in your answers to parts a. through f.) a. what is p(-1.46 < z < 0. response) b. what is p(0 < z < 1. response) c. what is p(z > -1. response) d. what is p(z < -2. response) e. what is p(z < 2. response) f. what is p(-2.58 < z < -1.1)?

a) 0.6636

b) 0.0951

c) 0,9474    

d)  0.0047

e) 0.9957  

f)   0.1308  

Step-by-step explanation:

We look in tables z values and then we see carefully aereas inside normal curve

a) P[- 1.46 < z < 0.63 ]     point 1.46 from table 0.0721  this s th area from value -1.46 to the left . And the value  z = 0.63  corresond to the area 0.7357 which includes the area between 1.46 to the left tail, then we have to subtarct and get 0.6636 .

P[- 1.46 < z < 0.63 ] = 0.6636             66.36 %

b) P [ 0 < z < 1.31 ] we just need the area for point 1.31   that is 0.0951

P [ 0 < z < 1.31 ] = 0.0951                   9.51 %

c)  P [z > - 1.62  ] = 1 - 0.0526

P [z > - 1.62  ] = 0,9474                       94.74 %

d) P[z < - 2.6 ] =   0.0047                       0.47 %

e) P [ z < 2.63 ] = 1 - 0.0043

P [ z < 2.63 ] = 0.9957                         99.57 %

f) P [ -2.58 < z < -1.1 ]  =  0.1357 - 0.0049 =  

P [ -2.58 < z < -1.1 ]  =  0.1308              13.08 %

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough