Answer:
a) 0.283 or 28.3%
b) 0.130 or 13%
c) 0.4 or 40%
d) 30.6 mm
Step-by-step explanation:
z-score of a single left atrial diameter value of healthy children can be calculated as:
z=
where
- X is the left atrial diameter value we are looking for its z-score
- M is the mean left atrial diameter of healthy children (26.7 mm)
- s is the standard deviation (4.7 mm)
Then
a) proportion of healthy children who have left atrial diameters less than 24 mm
=P(z<z*) where z* is the z-score of 24 mm
z*=
≈ −0.574
And P(z<−0.574)=0.283
b) proportion of healthy children who have left atrial diameters greater than 32 mm
= P(z>z*) = 1-P(z<z*) where z* is the z-score of 32 mm
z*=
≈ 1.128
1-P(z<1.128)=0.8703=0.130
c) proportion of healthy children have left atrial diameters between 25 and 30 mm
=P(z(25)<z<z(30)) where z(25), z(30) are the z-scores of 25 and 30 mm
z(30)=
≈ 0.702
z(25)=
≈ −0.362
P(z<0.702)=0.7587
P(z<−0.362)=0.3587
Then P(z(25)<z<z(30)) =0.7587 - 0.3587 =0.4
d) to find the value for which only about 20% have a larger left atrial diameter, we assume
P(z>z*)=0.2 or 20% where z* is the z-score of the value we are looking for.
Then P(z<z*)=0.8 and z*=0.84. That is
0.84=
solving this equation for X we get X=30.648
The value of a = 2.17 and b = 1.95.
<h3>What is regression line?</h3>
A regression line is a graphic representation of the regression equation expressing the hypothesized relationship between an outcome or dependent variable and one or more predictors or independent variables;
y=
Correlation:
r=0.964
R-squared:
r²=0.9292
Hence, value of a and b is 2.17 and 1.95.
learn more about regression line here:
brainly.com/question/11340674
#SPJ1
Answer:
70
Step-by-step explanation:
56+25%=70 (:
Answer: 
12.5
Step-by-step explanation: The triangle ABC and its altitude 
is represented in the figure below.
<u>Altitude</u> is a segment of line that link a vertex and the opposite side, forming a right angle.
So, because of , now we have two similar triangles, which means that ratios of corresponding sides are equal:
(1)
This is always true for a right triangle and a altitude drawn to the hypotenuse.
Triangle BDC is also right triangle. So, we can use Pythagorean theorem to determine the missing side.
(2)
Substituting (2) into (1):
We want to find f, so:
f = 7.5
The length of 
is
The length of the hypotenuse of triangle ABC is 12.5 units.
