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:

the circumference of a circle is, 10.676 cm.

step-by-step explanation:

the formula for circumference of a circle is given by:

where

c is the circumference of a circle and

d is the diameter of a circle.

given: diameter(d) = 3.4 cm and use

substitute these values in [1] we get;

cm

therefore, the circumference of a circle is, 10.676 cm