To evaluate the given probability we proceed as follows:
The z-score is given by:
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
from the question:
mean=272, sig=15
but the sample is n=36, thus we shall have:
√σ/n
=15/√36
=2.5
thus the z-score will be as follows:
x=272
z=(272-272)/2.5=0
x=274
z=(274-272)/2.5==0.8
thus
P(272<x<274)
=P(z<0.8)-P(z<0)
=0.7881-0.5
=0.2881
Hence the answer is 0.2881
The formulas are already given, all you have to do is plot them each separately and you will find that they crooks each other, the point of intersection is your solution.
Step 1; multiple equation 2 by -2: 14x+8y=-18
step2: subtract this new equation from equation 1 to eliminate x:
2y-8y=18-(-18)
-6y=36
y=-6
step 3: substitute y=6 in equation 2: -7x-4*(-6)=9, -7x=-15, x=15/7
A 10-foot ladder leans against a wall. It hits the wall 9 feet up. How far is the base of the ladder from the wall? Apply the Pythagorean Theorem to this problem
triangle
side S1 = 9 feet
hypotenuse H = 10 feet
side S2 - X = ?
the Pythagorean Theorem
H x H = S1 x S1 + S2 x S2 = S1 x S1 + X x X
X x X = H x H - S1 x S1 = 10 x 10 - 9 x 9 = 100 - 91 = 9
X x X = 9
X = 3
How far is the base of the ladder from the wall? 3 feet
check:
H x H = S1 x S1 + X x X
10 x 10 = 9 x 9 + 3 x 3
100 = 91 +9 = 100