Assume X is normally distributed with a mean of 12 and a standard deviation of 2.
Determine the value for x that solves each of the following. Round the answers to 2 decimal places.
(a) P(X > x) = 0.5
(b) P(X > x) = 0.95
(c) P(x < X < 12) = 0.2
(d) P( -x < X - 12 < x) = 0.95
(e) P( -x < X - 12 < x) = 0.99

a) x=12

b) x=8.71

c) x=10.95

d) x=3.92

e) x=5.152

Step-by-step explanation:

a) x=12.

To have a probability of 0.5, x must be the mean of X.

b) x=8.71

c) x=10.95

d) x=3.92

If we define Y=X-12, then

For z=1.96, the probability around the mean is 0.95. Then:

e) x=5.152

As in the question d, the area around the mean now is 0.99. This happens when z=2.576. Then:

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w