A set of middle school student heights are normally distributed with a mean of 150150150 centimeters and a standard deviation of 202020 centimeters. Let XXX represent the height of a randomly selected student from this set. Find P(X<115)P(X<115)P, left parenthesis, X, is less than, 115, right parenthesis.

0.04

Step-by-step explanation:

Given that :

Mean(m) = 150

Standard deviation (s) = 20

Find P(X<115)

Obtain the Zscore :

(x - m) / s

(115 - 150) / 20

P(X<115) = - 1.75

Using the Z probability calculator :

P(Z < - 1.75) = 0.040059

P(Z < - 1.75) = 0.04

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

its a straight line parallel to the time axis