Find the value of the probability of the standard normal variable Z corresponding to this area for problems 1-3.

Explained below.

Step-by-step explanation:

The complete question is:

Find the value of the probability of the standard normal variable Z corresponding to this area for problems 1-3.

1. P(Z < 1.62)

2. P(Z > -1.57)

3. P(-1.41 < Z < 0.63)

Solution:

Use Excel to solve the problems.

(1)

P(Z < 1.62)  =NORM.S.DIST(1.62,TRUE)

                 = 0.9474

(2)

P(Z > -1.57)  = P (Z < 1.57)

                  =NORM.S.DIST(1.57,TRUE)

                  = 0.9418

(3)

P(-1.41 < Z < 0.63) = P (Z < 0.63) - P (Z < -1.41)

                             =NORM.S.DIST(0.63,TRUE) - NORM.S.DIST(-1.41,TRUE)

                             = 0.7357 - 0.0793

                             = 0.6564

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560